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Tesi sul tema "Group actions"

Autore: Grafiati

Pubblicato: 4 giugno 2021

Ultima modifica: 25 luglio 2025

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1

Suabedissen, Rolf. "Topologizing group actions." Thesis, University of Oxford, 2006. http://ora.ox.ac.uk/objects/uuid:ca186b79-b4ea-423f-a697-5ed47b4672f9.

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This thesis is centered on the following question: Given an abstract group action by an Abelian group G on a set X, when is there a compact Hausdorff topology on X such that the group action is continuous? If such a topology exists, we call the group action compact-realizable. We show that if G is a locally-compact group, a necessary condition for a G-action to be compact-realizable, is that the image of X under the stabilizer map must be a compact subspace of the collection of closed subgroups of G equipped with the co-compact topology. We apply this result to give a complete characterization

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2

Chung, Kin Hoong School of Mathematics UNSW. "Compact Group Actions and Harmonic Analysis." Awarded by:University of New South Wales. School of Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17639.

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A large part of the structure of the objects in the theory of Dooley and Wildberger [Funktsional. Anal. I Prilozhen. 27 (1993), no. 1, 25-32] and that of Rouviere [Compositio Math. 73 (1990), no. 3, 241-270] can be described by considering a connected, finite-dimentional symmetric space G/H (as defined by Rouviere), with ???exponential map???, Exp, from L G/L H to G/H, an action, ???: K ??? Aut??(G) (where Aut?? (G) is the projection onto G/H of all the automorphisms of G which leave H invariant), of a Lie group, K, on G/H and the corresponding action, ???# , of K on L G/L H defined by g ??? L

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3

Klaus, Michele. "Group actions on homotopy spheres." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/35981.

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In the first part of the thesis we discuss the rank conjecture of Benson and Carlson. In particular, we prove that if G is a finite p-group of rank 3 and with p odd, or if G is a central extension of abelian p-groups, then there is a free finite G-CW-complex homotopy equivalent to the product of rk(G) spheres; where rk(G) is the rank of G. We also treat an extension of the rank conjecture to groups of finite virtual cohomological dimension. In this context, for p a fixed odd prime, we show that there is an infinite group L satisfying the two following properties: every finite subgroup G<L is

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4

Nica, Bogdan. "Group actions on median spaces." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=80342.

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We investigate a particular type of geometry, namely median metric spaces. This encompasses median graphs, as well as simple combinatorial structures known as spaces with walls.<br>The group-theoretic applications are towards the Kazhdan property and the Haagerup property.

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5

Morris, Gary. "Dynamical constraints on group actions." Thesis, University of East Anglia, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267775.

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6

Helsdon, Mark Andrew. "Group actions on real trees." Thesis, University of Cambridge, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.613233.

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7

Moseley, Daniel, and Daniel Moseley. "Group Actions on Hyperplane Arrangements." Thesis, University of Oregon, 2012. http://hdl.handle.net/1794/12373.

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In this dissertation, we will look at two families of algebras with connections to hyperplane arrangements that admit actions of finite groups. One of the fundamental questions to ask is how these decompose into irreducible representations. For the first family of algebras, we will use equivariant cohomology techniques to reduce the computation to an easier one. For the second family, we will use two decompositions over the intersection lattice of the hyperplane arrangement to aid us in computation.

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8

Posthuma, Hessel Bouke. "Quantization of Hamiltonian loop group actions." [S.l. : Amsterdam : s.n.] ; Universiteit van Amsterdam [Host], 2003. http://dare.uva.nl/document/70151.

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9

Clarkson, James Price. "Group actions on finite homotopy spheres." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/27134.

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Recently, Grodal and Smith [7}have developed a finite algebraic model to study hG-spaces where G is a finite group. The procedure associates to each G-space X with finite F_p homology a perfect chain complex of functors over the orbit category. When X has the homotopy type of a sphere, this construction is particularly well behaved. The reverse construction, building an hG-space from the algebraic model, generally produces an infinite dimensional space. In this thesis, we construct a finiteness obstruction for hG-spheres working one prime at a time. We then begin the development of a global

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10

Platten, Richard John. "Proper group actions on CW-complexes." Thesis, Queen Mary, University of London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.392890.

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11

Braven, Charles Frederick. "Cyclic homology, manifolds and group actions." Thesis, University of Exeter, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269737.

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12

Orem, Hendrik. "Fast Matrix Multiplication via Group Actions." Scholarship @ Claremont, 2009. https://scholarship.claremont.edu/hmc_theses/221.

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Recent work has shown that fast matrix multiplication algorithms can be constructed by embedding the two input matrices into a group algebra, applying a generalized discrete Fourier transform, and performing the multiplication in the Fourier basis. Developing an embedding that yields a matrix multiplication algorithm with running time faster than naive matrix multiplication leads to interesting combinatorial problems in group theory. The crux of such an embedding, after a group G has been chosen, lies in finding a triple of subsets of G that satisfy a certain algebraic relation. I show how the

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13

Belliart, Michel. "Actions de groupes de Lie sur les variétés compactes." Valenciennes, 1995. https://ged.uphf.fr/nuxeo/site/esupversions/9806b24c-e64d-4e28-b75a-6d3de2b5eb3a.

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Cette thèse est en deux parties. Dans la première partie, on énonce, justifie et montre partiellement la conjecture suivante : L'action localement libre de codimension 1, au moins deux fois continument différentiable et préservant le volume d'un groupe de Lie non-unimodulaire sur une variété compacte est conjuguée dans sa classe de différentiabilité à une action homogène. On fournit également des exemples de groupes auxquels ce résultat s'applique. Dans la seconde partie, on répond complètement au problème suivant, posé par J. F. Plante en 1986 : A quelles conditions un groupe de Lie connexe d

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14

Niederkrüger, Klaus. "Compact Lie group actions on contact manifolds." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975890360.

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15

Garcia, Armas Mario. "Group actions on curves over arbitrary fields." Thesis, University of British Columbia, 2015. http://hdl.handle.net/2429/52472.

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This thesis consists of three parts. The common theme is finite group actions on algebraic curves defined over an arbitrary field k. In Part I we classify finite group actions on irreducible conic curves defined over k. Equivalently, we classify finite (constant) subgroups of SO(q) up to conjugacy, where q is a nondegenerate quadratic form of rank 3 defined over k. In the case where k is the field of complex numbers, these groups were classified by F. Klein at the end of the 19th century. In recent papers of A. Beauville and X. Faber, this classification is extended to the case where k is arbi

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16

Yassawi, Reem. "Multiple mixing of local rank group actions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0015/NQ44636.pdf.

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17

Kutler, Max B. "Group Actions and Divisors on Tropical Curves." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/hmc_theses/5.

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Tropical geometry is algebraic geometry over the tropical semiring, or min-plus algebra. In this thesis, I discuss the basic geometry of plane tropical curves. By introducing the notion of abstract tropical curves, I am able to pass to a more abstract metric-topological setting. In this setting, I discuss divisors on tropical curves. I begin a study of $G$-invariant divisors and divisor classes.

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18

Yassawi, Reem Adel. "Multiple mixing of local rank group actions." Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=35655.

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Suppose G is a countable, Abelian group with an element of infinite order and let X be a mixing finite rank (rank r) action of G on a probability space, or let X be a mixing beta-local rank action of G with beta > 1/2. Suppose further that the Folner sequence { Fn } indexing the towers of the beta-local X satisfies a "bounded intersection property": there is a constant p such that each Fn can intersect no more than p disjoint translates of itself. If X is finite rank, we also suppose that the cardinalities of the r Folner sequences Fin ri=1 are comparable. We show that X is mixing of all order

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19

Potter, Rory. "Derived categories of surfaces and group actions." Thesis, University of Sheffield, 2017. http://etheses.whiterose.ac.uk/19643/.

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This thesis focuses on two distinct projects on the bounded derived category of coherent sheaves of surfaces and group actions from different directions. The first project studies bielliptic surfaces, which arise as quotients of products of elliptic curves by a finite group acting freely. We prove a structure theorem describing the group of exact autoequivalences of the bounded derived category of coherent sheaves on a bielliptic surface over C. We also list the generators of the group in some cases. The second project studies semi-orthogonal decompositions of the bounded equivariant derived c

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20

Joubert, Paul. "Geometric actions of the absolute Galois group." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/2508.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2006.<br>This thesis gives an introduction to some of the ideas originating from A. Grothendieck's 1984 manuscript Esquisse d'un programme. Most of these ideas are related to a new geometric approach to studying the absolute Galois group over the rationals by considering its action on certain geometric objects such as dessins d'enfants (called stick figures in this thesis) and the fundamental groups of certain moduli spaces of curves. I start by defining stick figures and explaining the connection between these innocent combinatoria

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21

Cotton, Michael R. "Abelian Group Actions and Hypersmooth Equivalence Relations." Thesis, University of North Texas, 2019. https://digital.library.unt.edu/ark:/67531/metadc1505289/.

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We show that any Borel action on a standard Borel space of a group which is topologically isomorphic to the sum of a countable abelian group with a countable sum of lines and circles induces an orbit equivalence relation which is hypersmooth. We also show that any Borel action of a second countable locally compact abelian group on a standard Borel space induces an orbit equivalence relation which is essentially hyperfinite, generalizing a result of Gao and Jackson for the countable abelian groups.

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22

DUMITRU, ALINA RALUCA. "COMPACT QUANTUM GROUP ACTIONS ON C*-ALGEBRAS." University of Cincinnati / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1178900803.

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23

Grecianu, Andrei-Paul. "Group actions on non-archimedean hyperbolic spaces." Thesis, McGill University, 2013. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=119392.

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We investigate group actions on a metric space that has some sort of hyperbolicity property. Such metric spaces can arise naturally in the study of hyperbolic, or relatively hyperbolic, groups and of systems of equations over them. We will establish a classification of isometries for non-archimedean hyperbolic spaces similar to that of isometries of classical hyperbolic spaces, various quasi-isometric embeddings of non-geodesic hyperbolic spaces into geodesic ones and a criterion for a group acting on a hyperbolic space to be hyperbolic relative to a point stabilizer. We shall then use these r

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24

Sandfeldt, Sven. "Local Rigidity of Some Lie Group Actions." Thesis, KTH, Matematik (Avd.), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-272842.

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In this paper we study local rigidity of actions of simply connected Lie groups. In particular, we apply the Nash-Moser inverse function theorem to give sufficient conditions for the action of a simply connected Lie group to be locally rigid. Let $G$ be a Lie group, $H < G$ a simply connected subgroup and $\Gamma < G$ a cocompact lattice. We apply the result for general actions of simply connected groups to obtain sufficient conditions for the action of $H$ on $\Gamma\backslash G$ by right translations to be locally rigid. We also discuss some possible applications of this sufficient con

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25

Iverson, Joseph. "Frames Generated by Actions of Locally Compact Groups." Thesis, University of Oregon, 2016. http://hdl.handle.net/1794/20443.

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Let $G$ be a second countable, locally compact group which is either compact or abelian, and let $\rho$ be a unitary representation of $G$ on a separable Hilbert space $\mathcal{H}_\rho$. We examine frames of the form $\{ \rho(x) f_j \colon x \in G, j \in I\}$ for families $\{f_j\}_{j \in I}$ in $\mathcal{H}_\rho$. In particular, we give necessary and sufficient conditions for the joint orbit of a family of vectors in $\mathcal{H}_\rho$ to form a continuous frame. We pay special attention to this problem in the setting of shift invariance. In other words, we fix a larger second countable loc

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26

Kenneally, Darren John. "On eigenvectors for semisimple elements in actions of algebraic groups." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/224782.

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Let G be a simple simply connected algebraic group defined over an algebraically closed field K and V an irreducible module defined over K on which G acts. Let E denote the set of vectors in V which are eigenvectors for some non-central semisimple element of G and some eigenvalue in K*. We prove, with a short list of possible exceptions, that the dimension of Ē is strictly less than the dimension of V provided dim V > dim G + 2 and that there is equality otherwise. In particular, by considering only the eigenvalue 1, it follows that the closure of the union of fixed point spaces of non-centra

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27

Wein, Alexander Spence. "Statistical estimation in the presence of group actions." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/117314.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 199-210).<br>Imagine we want to recover an unknown vector given many noisy copies of it, except each copy is cyclically shifted by an unknown offset (this is "multi-reference alignment"). Or imagine we want to reconstruct an unknown 3D structure (e.g. a molecule) given many noisy pictures of it taken from different unknown angles (this is "cryo-EM"). These problems (and many others) involve the action of unknown group ele

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28

Jarrett, Kieran. "Non-singular actions of countable groups." Thesis, University of Bath, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761021.

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In this thesis we study actions of countable groups on measure spaces underthe assumption that the dynamics are non-singular, with particular reference topointwise ergodic theorems and their relationship to the critical dimensions ofthe action.

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29

Baumgaertel, H., A. L. Carey, and Andreas Cap@esi ac at. "Hilbert C*-systems for Actions of the Circle Group." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi940.ps.

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30

Björklund, Michael. "Limit Theorems for Ergodic Group Actions and Random Walks." Doctoral thesis, KTH, Matematik (Inst.), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10451.

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This thesis consists of an introduction, a summary and 7 papers. The papers are devoted to problems in ergodic theory, equidistribution on compact manifolds and random walks on groups. In Papers A and B, we generalize two classical ergodic theorems for actions of abelian groups. The main result is a generalization of Kingman’s subadditive ergodic theorem to ergodic actions of the group Zd. In Papers C,D and E, we consider equidistribution problems on nilmanifolds. In Paper C we study the asymptotic behavior of dilations of probability measures on nilmanifolds, supported on singular sets, and p

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31

Madore, Blair F. "Rank-one group actions with simple mixing Z subactions." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ49929.pdf.

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32

Kirsebom, Maxim Solund. "Extreme value theory for group actions on homogeneous spaces." Thesis, University of Bristol, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.664970.

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In this thesis we study extreme value theory for random walks as well as one-parameter actions on homogeneous spaces. In both cases we investigate the limiting distributions for the maximum of an observable evaluated along a trajectory of the system. In particular we are going to consider asymptotic distributions for closest distance returns to a given point· and tor maximal excursions to the cusp. For closest returns on the torus we establish an exact extreme value distribution while for other cases we obtain estimates on the extreme value distributions for sparse sequences. For random walks

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33

Björklund, Michael. "Limit theorems for ergodic group actions and random walks /." Stockholm : Matematik, Skolan för teknikvetenskap, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10451.

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34

Birembaux, Olivier. "Actions de groupes résolubles scindement de f-fibres hermitiens." Valenciennes, 1997. https://ged.uphf.fr/nuxeo/site/esupversions/b7bd7233-5e92-4465-8cce-ff9ef4078593.

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Première partie : Soient G un groupe de Lie connexe de dimension n - 1, f une action localement libre de classe Cr (avec r supérieure ou égale à 2) de G sur une variété compacte M de dimension n supérieure ou égale a 3. Nous supposons qu'il existe dans l'algèbre de Lie de G un champ Y tel que la partie réelle de chaque valeur propre de ad(Y) soit strictement plus petite que 0. Alors, nous montrons que f est Cr -conjuguée à une action modèle de G sur un espace homogène H/T ou H est un groupe de Lie contenant G. Nos hypothèses impliquent que G a une structure particulière, mais il existe quand m

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35

Cannizzo, Jan. "Schreier Graphs and Ergodic Properties of Boundary Actions." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31444.

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This thesis is broadly concerned with two problems: investigating the ergodic properties of boundary actions, and investigating various properties of Schreier graphs. Our main result concerning the former problem is that, in a variety of situations, the action of an invariant random subgroup of a group G on a boundary of G (e.g. the hyperbolic boundary, or the Poisson boundary) is conservative (there are no wandering sets). This addresses a question asked by Grigorchuk, Kaimanovich, and Nagnibeda and establishes a connection between invariant random subgroups and normal subgroups. We approach

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36

Lange, Carsten. "Combinatorial curvatures, group actions, and colourings: aspects of topological combinatorics." [S.l.] : [s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=973473487.

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37

Yabu, Yoshiro. "Geometric Study of Classical and Quantum Systems with Group Actions." 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/123853.

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38

SADE, MARTIN CHARLES. "VARIATIONAL PRINCIPLES FOR FIELD VARIABLES SUBJECT TO GROUP ACTIONS (GAUGE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/188075.

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This dissertation is concerned with variational problems whose field variables are functions on a product manifold M x G of two manifolds M and G. These field variables transform as type (0,1) tensor fields on M and are denoted by ψ(h)ᵅ (h = 1, ..., n = dim M, α = 1, ..., r = dim G). The dependence of ψ(h)ᵅ on the coordinates of G is given by a generalized gauge transformation that depends on a local map h:M → G. The requirement that a Lagrangian that is defined in terms of these field variables be independent of the coordinates of G and the choice of the map h endows G with a local Lie group

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39

Wong, Ming Lai. "Q-Fourier transform, q-Heisenberg algebra and quantum group actions /." View Abstract or Full-Text, 2003. http://library.ust.hk/cgi/db/thesis.pl?MATH%202003%20WONG.

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40

Tarzi, Sam. "Group actions on amorphous sets and reducts of coloured ransom graphs." Thesis, Queen Mary, University of London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.406911.

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41

Alsaody, Seidon. "A Categorical Study of Composition Algebras via Group Actions and Triality." Doctoral thesis, Uppsala universitet, Algebra och geometri, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-248519.

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A composition algebra is a non-zero algebra endowed with a strictly non-degenerate, multiplicative quadratic form. Finite-dimensional composition algebras exist only in dimension 1, 2, 4 and 8 and are in general not associative or unital. Over the real numbers, such algebras are division algebras if and only if they are absolute valued, i.e. equipped with a multiplicative norm. The problem of classifying all absolute valued algebras and, more generally, all composition algebras of finite dimension remains unsolved. In dimension eight, this is related to the triality phenomenon. We approach thi

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42

Vigolo, Federico. "Geometry of actions, expanders and warped cones." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:0b094203-6f94-4b3b-826e-c8b1ac6203b8.

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In this thesis we introduce a notion of graphs approximating actions of finitely generated groups on metric and measure spaces. We systematically investigate expansion properties of said graphs and we prove that a sequence of graphs approximating a fixed action ρ forms a family of expanders if and only if ρ is expanding in measure. This enables us to rely on a number of known results to construct numerous new families of expander (and superexpander) graphs. Proceeding in our investigation, we show that the graphs approximating an action are uniformly quasi-isometric to the level sets of the as

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43

Ericsson, Sandra, and Marielle Frid. "Suggested actions to improve the warehouse layout at Nordic E-commerce group." Thesis, Linnéuniversitetet, Institutionen för ekonomistyrning och logistik (ELO), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-26740.

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Background: Nordic E-commerce group (NECG) consists of affiliated companies NordicInk, NordicFeel and PetsOnline. Three different types of companies in one warehouse area contribute to a wide range of products held in inventory. NECG’s problem derives in the fact that the company’s warehouse layout needs to handle a larger volume of sales, but is not capable of doing this in a structured way today. This matter of fact has led to new thoughts concerning improvements of the layout. The warehouse layout referred to in this thesis includes input and output doors, receiving and outgoing areas, mate

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44

Lenhardt, Fabian [Verfasser]. "The Baum-Connes conjecture, Swan group actions and controlled topology / Fabian Lenhardt." Berlin : Freie Universität Berlin, 2013. http://d-nb.info/1031106510/34.

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45

Tait, Joseph. "Group actions on differentials of curves and cohomology bases of hyperelliptic curves." Thesis, University of Southampton, 2014. https://eprints.soton.ac.uk/373877/.

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46

Mazur, Justin D. "Motivic zeta-functions and the Grothendieck ring for varieties with group actions." [Bloomington, Ind.] : Indiana University, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3354903.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2009.<br>Title from PDF t.p. (viewed on Feb. 4, 2010). Source: Dissertation Abstracts International, Volume: 70-04, Section: B, page: 2339. Adviser: Valery Lunts.

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47

Raizada, Rachana. "Corporate responses to government and environmental group actions designed to protect the environment." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ27230.pdf.

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48

Ash, David B. "Transformational leadership and organizational learning : leader actions that stimulate individual and group learning." Virtual Press, 1997. http://liblink.bsu.edu/uhtbin/catkey/1063425.

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Abstract (sommario):

The purpose of this research was to identify and describe the action's leaders practice that stimulate individual and group learning. An MLQ- Multifactor Leadership Questionnaire and a series of interviews with members of three work teams were utilized to gather research data. This is one of the first studies completed to research this important aspect of leadership. In all three cases, the teams shared experiences where learning was transformed into useable knowledge to accomplish objectives or solve problems. The three teams learned and generated new knowledge based on viewing, challenging,

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49

Ramasu, Pako. "Internal monoid actions in a cartesian closed category and higher-dimensional group automorphisms." Doctoral thesis, University of Cape Town, 2015. http://hdl.handle.net/11427/20248.

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The notion of cat¹-group which was introduced by Loday is equivalent to the notions of crossed module and of internal category in the category of groups. This notion of cat¹-groups and their morphisms admits natural generalization to catⁿ-groups, which give rise to n-fold categories in the category of groups. There is also a characterization of catⁿ-groups in terms of crossed n-cubes which was given by Ellis and Steiner. The category Catⁿ (Groups) of internal n-fold categories in the category of groups is a cartesian closed category, however given an object X in Catⁿ (Groups), calculating corr

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50

Hedén, Isac. "Ga-actions on Complex Affine Threefolds." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-203708.

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This thesis consists of two papers and a summary. The papers both deal with affine algebraic complex varieties, and in particular such varieties in dimension three that have a non-trivial action of one of the one-dimensional algebraic groups Ga := (C, +) and Gm := (C*, ·). The methods used involve blowing up of subvarieties, the correspondances between Ga - and Gm - actions on an affine variety X with locally nilpotent derivations and Z-gradings respectively on O(X) and passing from a filtered algebra A to its associated graded algebra gr(A). In Paper

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