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Relevant bibliographies by topics / Nilpotent and solvable Lie groups

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Academic literature on the topic 'Nilpotent and solvable Lie groups'

Author: Grafiati

Published: 17 September 2021

Last updated: 18 February 2022

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Journal articles on the topic "Nilpotent and solvable Lie groups"

1

Lipsman, R. L. "Restricting Representations of Completely Solvable Lie Groups." Canadian Journal of Mathematics 42, no. 5 (1990): 790–824. http://dx.doi.org/10.4153/cjm-1990-042-9.

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We are concerned here with the problem of describing the direct integral decomposition of a unitary representation obtained by restriction from a larger group. This is the dual problem to the more commonly investigated problem of decomposing induced representations. In this paper we work in the context of completely solvable Lie groups—more general than nilpotent, but less general than exponential solvable. Moreover, the groups involved are simply connected. The restriction problem was considered originally in [2] and in [6] for nilpotent groups.

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Deré, Jonas, and Marcos Origlia. "Simply transitive NIL-affine actions of solvable Lie groups." Forum Mathematicum 33, no. 5 (2021): 1349–67. http://dx.doi.org/10.1515/forum-2020-0114.

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Abstract Every simply connected and connected solvable Lie group 𝐺 admits a simply transitive action on a nilpotent Lie group 𝐻 via affine transformations. Although the existence is guaranteed, not much is known about which Lie groups 𝐺 can act simply transitively on which Lie groups 𝐻. So far, the focus was mainly on the case where 𝐺 is also nilpotent, leading to a characterization depending only on the corresponding Lie algebras and related to the notion of post-Lie algebra structures. This paper studies two different aspects of this problem. First, we give a method to check whether a given

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3

GUDMUNDSSON, SIGMUNDUR, and MARTIN SVENSSON. "Harmonic morphisms from solvable Lie groups." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 2 (2009): 389–408. http://dx.doi.org/10.1017/s0305004109002564.

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AbstractIn this paper we introduce two new methods for constructing harmonic morphisms from solvable Lie groups. The first method yields global solutions from any simply connected nilpotent Lie group and from any Riemannian symmetric space of non-compact type and rank r ≥ 3. The second method provides us with global solutions from any Damek–Ricci space and many non-compact Riemannian symmetric spaces. We then give a continuous family of 3-dimensional solvable Lie groups not admitting any complex-valued harmonic morphisms, not even locally.

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4

Aka, Menny, Emmanuel Breuillard, Lior Rosenzweig, and Nicolas de Saxcé. "Diophantine properties of nilpotent Lie groups." Compositio Mathematica 151, no. 6 (2015): 1157–88. http://dx.doi.org/10.1112/s0010437x14007854.

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A finitely generated subgroup ${\rm\Gamma}$ of a real Lie group $G$ is said to be Diophantine if there is ${\it\beta}>0$ such that non-trivial elements in the word ball $B_{{\rm\Gamma}}(n)$ centered at $1\in {\rm\Gamma}$ never approach the identity of $G$ closer than $|B_{{\rm\Gamma}}(n)|^{-{\it\beta}}$. A Lie group $G$ is said to be Diophantine if for every $k\geqslant 1$ a random $k$-tuple in $G$ generates a Diophantine subgroup. Semi-simple Lie groups are conjectured to be Diophantine but very little is proven in this direction. We give a characterization of Diophantine nilpotent Lie gro

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5

Bajo, Ignacio. "Isotropy of non-nilpotent Riemannian solvable Lie groups." Annals of Global Analysis and Geometry 14, no. 1 (1996): 61–67. http://dx.doi.org/10.1007/bf00128195.

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6

Chen, Yin, and Runxuan Zhang. "SOME VARIETIES OF LIE RINGS." Asian-European Journal of Mathematics 05, no. 04 (2012): 1250051. http://dx.doi.org/10.1142/s1793557112500519.

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In this paper, several theorems of Macdonald [On certain varieties of groups, Math. Z.76 (1961) 270–282; On certain varieties of groups II, Math. Z.78 (1962) 175–188] on the varieties of nilpotent groups will be generalized to the case of Lie rings. We consider three varieties of Lie rings of any characteristic associated with some equations (see Eqs. (1.1)–(1.3)). We prove that each Lie ring in variety (1.1) is nilpotent of exponent at most n + 2; if L is a Lie ring in variety (1.2), then L2 is nilpotent of exponent at most n + 1; and each Lie ring in variety (1.3) is solvable of length at mo

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7

Dekimpe, Karel. "On polynomial products in nilpotent and solvable Lie groups." Proceedings of the American Mathematical Society 131, no. 3 (2002): 973–78. http://dx.doi.org/10.1090/s0002-9939-02-06572-3.

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MOSAK, RICHARD, and MARTIN MOSKOWITZ. "Lattices in a split solvable Lie group." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 2 (1997): 245–50. http://dx.doi.org/10.1017/s0305004196001582.

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Given a Lie group, it is often useful to have a parametrization of the set of its lattices. In Euclidean space ℝn, for example, each lattice corresponds to a basis, and any lattice is equivalent to the standard integer lattice under an automorphism in GL(n, ℝ). In the nilpotent case, the lattices of the Heisenberg groups are classified, up to automorphisms, by certain sequences of positive integers with divisibility conditions (see [1]). In this paper we will study the set of lattices in a class of simply connected, solvable, but not nilpotent groups G. The construction of G depends on a diago

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9

Suciu, Alexander I., and He Wang. "Formality properties of finitely generated groups and Lie algebras." Forum Mathematicum 31, no. 4 (2019): 867–905. http://dx.doi.org/10.1515/forum-2018-0098.

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Abstract We explore the graded-formality and filtered-formality properties of finitely generated groups by studying the various Lie algebras over a field of characteristic 0 attached to such groups, including the Malcev Lie algebra, the associated graded Lie algebra, the holonomy Lie algebra, and the Chen Lie algebra. We explain how these notions behave with respect to split injections, coproducts, direct products, as well as field extensions, and how they are inherited by solvable and nilpotent quotients. A key tool in this analysis is the 1-minimal model of the group, and the way this model

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Saxcé, Nicolas. "SUBGROUPS OF FRACTIONAL DIMENSION IN NILPOTENT OR SOLVABLE LIE GROUPS." Mathematika 59, no. 2 (2013): 497–511. http://dx.doi.org/10.1112/s0025579313000077.

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Dissertations / Theses on the topic "Nilpotent and solvable Lie groups"

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Santos, Edson Carlos Licurgo. "Estruturas complexas comauto-espaços nilpotentes e soluveis." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305823.

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Orientador: Luiz Antonio Barrera San Martin<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-10T11:48:47Z (GMT). No. of bitstreams: 1 Santos_EdsonCarlosLicurgo_D.pdf: 405695 bytes, checksum: 334d5172d85f7bc35539dbd900fbef67 (MD5) Previous issue date: 2007<br>Resumo: Seja (g; [·,·]) uma álgebra de Lie com uma estrutura complexa integrável J. Os ± i-auto-espaços de J são subálgebras complexas de gC isomorfas a álgebra (g; [*]J ) com colchete [X * Y ]J = ½ ([X, Y ] - [JX, JY ]). Considera

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2

Zergane, Amel. "Séparation des représentations des groupes de Lie par des ensembles moments." Thesis, Dijon, 2011. http://www.theses.fr/2011DIJOS086/document.

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Si (π, H) est une représentation unitaire irréductible d'un groupe de Lie G, on sait lui associer son application moment Ψπ. La fermeture de l'image de Ψπ s'appelle l'ensemble moment de π. Généralement, cet ensemble est Conv(Oπ), si Oπ est l'orbite coadjointe associée à π. Mais il ne caractérise pas π : deux orbites distinctes peuvent avoir la même enveloppe convexe fermée. On peut contourner cette non séparation en considérant un surgroupe G+ de G et une application non linéaire ø de g* dans (g+)* telle que, pour les orbites générique, ø(O) est une orbite et Conv (ø(O)) caractérise O. Dans ce

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Talley, Amanda Renee. "An Introduction to Lie Algebra." CSUSB ScholarWorks, 2017. https://scholarworks.lib.csusb.edu/etd/591.

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An (associative) algebra is a vector space over a field equipped with an associative, bilinear multiplication. By use of a new bilinear operation, any associative algebra morphs into a nonassociative abstract Lie algebra, where the new product in terms of the given associative product, is the commutator. The crux of this paper is to investigate the commutator as it pertains to the general linear group and its subalgebras. This forces us to examine properties of ring theory under the lens of linear algebra, as we determine subalgebras, ideals, and solvability as decomposed into an extension of

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Milian, Dagmara. "Locally nilpotent 5-Engel p-groups." Thesis, University of Oxford, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.561122.

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In this thesis we investigate the structure of locally nilpotent 5-Engel p-groups. We show that for p > 7, locally nilpotent 5-Engel p-groups have class at most 10. This is a global theorem, where the result is not dependent on the number of generators of the group. The proof uses new and established Lie methods and a custom C++ implementation of an algorithm that constructs minimal generating sets and structure constants of multi- graded Lie algebras in a variety defined by three multilinear relations, which hold in the Lie rings associated with 5-Engel p-groups. We obtain our results by calc

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Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.

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The conjugacy length function of a group Γ determines, for a given a pair of conjugate elements u,v ∈ Γ, an upper bound for the shortest γ in Γ such that uγ = γv, relative to the lengths of u and v. This thesis focuses on estimating the conjugacy length function in certain finitely generated groups. We first look at a collection of solvable groups. We see how the lamplighter groups have a linear conjugacy length function; we find a cubic upper bound for free solvable groups; for solvable Baumslag--Solitar groups it is linear, while for a larger family of abelian-by-cyclic groups we get either

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Nevins, Monica 1973. "Admissible nilpotent coadjoint orbits of p-adic reductive Lie groups." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47467.

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Snopçe, Ilir. "Lie methods in pro-p groups." Diss., Online access via UMI:, 2009.

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8

Wood, Lisa M. "ON THE SOLVABLE LENGTH OF ASSOCIATIVE ALGEBRAS, MATRIX GROUPS, AND LIE ALGEBRAS." NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-10272004-164622/.

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Let A be an algebraic system with product a*b between elements a and b in A. It is of interest to compare the solvable length t with other invariants, for instance size, order, or dimension of A. Thus we ask, for a given t what is the smallest n such that there is an A of length t and invariant n. It is this problem that we consider for associative algebras, matrix groups, and Lie algebras. We consider A in each case to be subsets of (strictly) upper triangular n by n matrices. Then the invariant is n. We do these for the associative (Lie) algebras of all strictly upper triangular n by n matri

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9

Achar, Pramod Narahari 1976. "Equivariant coherent sheaves on the nilpotent cone for complex reductive Lie groups." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8642.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.<br>Includes bibliographical references (p. 71).<br>Let G be a connected complex reductive Lie group. We propose a certain bijection between the set of dominant integral weights of G, and the set of pairs consisting of a nilpotent coadjoint orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit. A constructive proof of this bijection is given for the groups GL(n, C), and the bijection is established by direct calculation in a handful of particular groups. Partial progress is

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10

Mohammed, Zakiyah. "Carter Subgroups and Carter's Theorem." Youngstown State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1310158687.

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Books on the topic "Nilpotent and solvable Lie groups"

1

Goze, Michel. Nilpotent Lie algebras. Kluwer Academic, 1996.

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Fischer, Veronique, and Michael Ruzhansky. Quantization on Nilpotent Lie Groups. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29558-9.

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New developments in Lie theory and its applications: Seventh workshop in Lie theory and its applications, November 26-December 1, 2000, Cordoba, Argentina. American Mathematical Society, 2011.

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4

P, Greenleaf Frederick, ed. Representations of nilpotent Lie groups and their applications. Cambridge University Press, 1990.

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Fujiwara, Hidenori, and Jean Ludwig. Harmonic Analysis on Exponential Solvable Lie Groups. Springer Japan, 2015. http://dx.doi.org/10.1007/978-4-431-55288-8.

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6

1959-, McGovern William M., ed. Nilpotent orbits in semisimple Lie algebras. Van Nostrand Reinhold, 1993.

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7

author, Winternitz Pavel, ed. Classification and identification of Lie algebras. American Mathematical Society, 2014.

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8

Finite presentability of S-arithmetic groups: Compact presentability of solvable groups. Springer-Verlag, 1987.

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9

Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory. Longman Scientific & Technical, 1986.

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Schempp, W. Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory. Longman Scientific & Technical, 1986.

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Book chapters on the topic "Nilpotent and solvable Lie groups"

1

San Martin, Luiz A. B. "Solvable and Nilpotent Groups." In Lie Groups. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61824-7_10.

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2

Hilgert, Joachim, and Karl-Hermann Neeb. "Normal Subgroups, Nilpotent and Solvable Lie Groups." In Springer Monographs in Mathematics. Springer New York, 2012. http://dx.doi.org/10.1007/978-0-387-84794-8_11.

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3

Taylor, Michael. "Nilpotent Lie groups." In Mathematical Surveys and Monographs. American Mathematical Society, 1986. http://dx.doi.org/10.1090/surv/022/07.

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Machì, Antonio. "Nilpotent Groups and Solvable Groups." In UNITEXT. Springer Milan, 2012. http://dx.doi.org/10.1007/978-88-470-2421-2_5.

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Isaacs, I. "Solvable and nilpotent groups." In Graduate Studies in Mathematics. American Mathematical Society, 2009. http://dx.doi.org/10.1090/gsm/100/08.

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Roman, Steven. "Solvable and Nilpotent Groups." In Fundamentals of Group Theory. Birkhäuser Boston, 2011. http://dx.doi.org/10.1007/978-0-8176-8301-6_11.

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Kirillov, A. "Solvable Lie groups." In Graduate Studies in Mathematics. American Mathematical Society, 2004. http://dx.doi.org/10.1090/gsm/064/04.

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Serre, Jean-Pierre. "Nilpotent and Solvable Lie Algebras." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-540-70634-2_5.

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9

Serre, Jean-Pierre. "Nilpotent Lie Algebras and Solvable Lie Algebras." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56884-8_1.

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Serre, Jean-Pierre. "Nilpotent Lie Algebras and Solvable Lie Algebras." In Complex Semisimple Lie Algebras. Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-3910-7_1.

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Conference papers on the topic "Nilpotent and solvable Lie groups"

1

BARBERIS, MARÍA LAURA. "HYPERCOMPLEX STRUCTURES ON SPECIAL CLASSES OF NILPOTENT AND SOLVABLE LIE GROUPS." In Proceedings of the Second Meeting. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810038_0001.

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2

Zargeh, Chia. "A note on solvable and nilpotent Lie algebras." In The First Regional Conference on the Advanced Mathematics and Its Applications. Ispacs GmbH, 2012. http://dx.doi.org/10.5899/2012/cjac-001-017.

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Currey, Brad, Azita Mayeli, and Vignon Oussa. "Sampling and interpolation on certain nilpotent lie groups." In 2015 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2015. http://dx.doi.org/10.1109/sampta.2015.7148853.

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Feinsilver, Philip, Uwe Granz, and René Schott. "On the computation of polynomial representations of nilpotent Lie groups." In the 1997 ACM symposium. ACM Press, 1997. http://dx.doi.org/10.1145/331697.332345.

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Ballesteros, A., A. Blasco, and F. Musso. "Lotka-Volterra systems as Poisson-Lie dynamics on solvable groups." In XX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. AIP, 2012. http://dx.doi.org/10.1063/1.4733365.

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Beltiţă, I., D. Beltiţă, Piotr Kielanowski, et al. "A Survey on Weyl Calculus for Representations of Nilpotent Lie Groups." In XXVIII WORKSHOP ON GEOMETRICAL METHODS IN PHYSICS. AIP, 2009. http://dx.doi.org/10.1063/1.3275600.

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BAKLOUTI, Ali, Hidenori FUJIWARA, and Jean LUDWIG. "A variant of the Frobenius reciprocity for restricted representations on nilpotent Lie groups." In Proceedings of the Fourth German–Japanese Symposium. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812832825_0002.

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Becker-Kern, P., and W. Hazod. "Mehler hemigroups and embedding of discrete skew convolution semigroups on simply connected nilpotent Lie groups." In Proceedings of the Fourth German–Japanese Symposium. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812832825_0003.

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Reports on the topic "Nilpotent and solvable Lie groups"

1

Ikawa, Osamu. Motion of Charged Particles in Two-Step Nilpotent Lie Groups. GIQ, 2012. http://dx.doi.org/10.7546/giq-12-2011-252-262.

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Ikawa, Osamu. Motion of Charged Particles in Two-Step Nilpotent Lie Groups. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-20-2010-57-67.

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