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Relevant bibliographies by topics / Quaternionic group

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Academic literature on the topic 'Quaternionic group'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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Journal articles on the topic "Quaternionic group"

1

Pap, Margit, and Ferenc Schipp. "Quaternionic Blaschke Group." Mathematics 7, no. 1 (2018): 33. http://dx.doi.org/10.3390/math7010033.

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In the complex case, the Blaschke group was introduced and studied. It turned out that in the complex case this group plays important role in the construction of analytic wavelets and multiresolution analysis in different analytic function spaces. The extension of the wavelet theory to quaternion variable function spaces would be very beneficial in the solution of many problems in physics. A first step in this direction is to give the quaternionic analogue of the Blaschke group. In this paper we introduce the quaternionic Blaschke group and we study the properties of this group and its subgrou

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Rahmawati, Latief, Muhammad Ardhi Khalif, and Muhammad Farchani Rosyid. "Quaternionic Version of Rotation Groups." Journal Of Natural Sciences And Mathematics Research 1, no. 1 (2015): 17. http://dx.doi.org/10.21580/jnsmr.2015.1.1.479.

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<p>Quaternionic version of rotation group SO(3) has been constructed. We construct<br />a quatenionic version of rotation operation that act to a quaternionic version of a<br />space coordinate vector. The computation are done for every rotation about each<br />coordinate axes (x,y, and z). The rotated quaternionic space coordinate vector con-<br />tain some unknown constants which determine the quaternionic rotation operator.<br />By solving for that constants, we get the expression of the quaternionics version<br />of the rotation operator. Finally t

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HANLON, B. E., and G. C. JOSHI. "SPONTANEOUS CP VIOLATION FROM A QUATERNIONIC KALUZA–KLEIN THEORY." International Journal of Modern Physics A 08, no. 19 (1993): 3263–83. http://dx.doi.org/10.1142/s0217751x93001314.

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Motivated by the isomorphism between the universal covering group of the six-dimensional Lorentz group and the special linear group over the quaternions, a locally quaternionic covariant theory is postulated to exist in six space–time dimensions. Compactifying onto the space–time M4 ⊗ S2 a complex theory is retrieved on the four-dimensional Minkowski space with the essential quaternionic nature confined to S2. Quaternionic spinors are introduced and a dimensionally reduced theory recovered which exhibits a CP-violating effect via spontaneous symmetry breaking.

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Koca, Nazife Özdeş, Mehmet Koca, and Muna Al-Sawafi. "FCC, BCC and SC Lattices Derived from the Coxeter-Weyl groups and quaternions." Sultan Qaboos University Journal for Science [SQUJS] 19, no. 1 (2014): 95. http://dx.doi.org/10.24200/squjs.vol19iss1pp95-104.

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We construct the fcc (face centered cubic), bcc (body centered cubic) and sc (simple cubic) lattices as the root and the weight lattices of the affine extended Coxeter groups W(A3) and W(B3)=Aut(A3). It is naturally expected that these rank-3 Coxeter-Weyl groups define the point tetrahedral symmetry and the octahedral symmetry of the cubic lattices which have extensive applications in material science. The imaginary quaternionic units are used to represent the root systems of the rank-3 Coxeter-Dynkin diagrams which correspond to the generating vectors of the lattices of interest. The group el

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Chauhan, Bhupendra C. S., Pawan Kumar Joshi, and O. P. S. Negi. "Quaternion generalization of super-Poincaré group." International Journal of Modern Physics A 34, no. 01 (2019): 1950006. http://dx.doi.org/10.1142/s0217751x19500064.

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Super-Poincaré algebra in [Formula: see text] space–time dimensions has been studied in terms of quaternionic representation of Lorentz group. Starting the connection of quaternion Lorentz group with [Formula: see text] group, the [Formula: see text] spinors for Dirac and Weyl representations of Poincaré group are described consistently to extend the Poincaré algebra to super-Poincaré algebra for [Formula: see text] space–time.

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GONGOPADHYAY, KRISHNENDU, ABHISHEK MUKHERJEE та SUJIT KUMAR SARDAR. "TEST MAP AND DISCRETENESS IN SL(2, ℍ)". Glasgow Mathematical Journal 61, № 03 (2018): 523–33. http://dx.doi.org/10.1017/s0017089518000332.

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AbstractLet ℍ be the division ring of real quaternions. Let SL(2, ℍ) be the group of 2 × 2 quaternionic matrices $A={\scriptsize{(\begin{array}{l@{\quad}l} a &amp; b \\ c &amp; d \end{array})}}$ with quaternionic determinant det A = |ad − aca−1b| = 1. This group acts by the orientation-preserving isometries of the five-dimensional real hyperbolic space. We obtain discreteness criteria for Zariski-dense subgroups of SL(2, ℍ).

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Alpay, Daniel, Fabrizio Colombo, Jonathan Gantner, and David P. Kimsey. "Functions of the infinitesimal generator of a strongly continuous quaternionic group." Analysis and Applications 15, no. 02 (2017): 279–311. http://dx.doi.org/10.1142/s021953051650007x.

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The quaternionic analogue of the Riesz–Dunford functional calculus and the theory of semigroups and groups of linear quaternionic operators have recently been introduced and studied. In this paper, we suppose that [Formula: see text] is the quaternionic infinitesimal generator of a strongly continuous group of operators [Formula: see text] and we show how we can define bounded operators [Formula: see text], where [Formula: see text] belongs to a class of functions that is larger than the one to which the quaternionic functional calculus applies, using the quaternionic Laplace–Stieltjes transfo

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Scolarici, G., and L. Solombrino. "Notes on quaternionic group representations." International Journal of Theoretical Physics 34, no. 12 (1995): 2491–500. http://dx.doi.org/10.1007/bf00670780.

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Faress, Moussa, and Said Fahlaoui. "Beurling’s theorem for quaternionic Heisenberg group." Journal of Analysis 29, no. 3 (2021): 1043–54. http://dx.doi.org/10.1007/s41478-020-00294-2.

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Qin, Huani, Yueping Jiang, and Wensheng Cao. "Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/684594.

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We obtain an analogue of Jørgensen's inequality in quaternionic hyperbolic space. As an application, we prove that if ther-generator quaternionic Kleinian group satisfies I-condition, then its algebraic limit is also a quaternionic Kleinian group. Our results are generalizations of the counterparts in then-dimensional real hyperbolic space.

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Dissertations / Theses on the topic "Quaternionic group"

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Boote, Yumi. "On the symmetric square of quaternionic projective space." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/on-the-symmetric-square-of-quaternionic-projective-space(9ac64fc3-60b7-449e-8f5a-264a62b1429b).html.

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The main purpose of this thesis is to calculate the integral cohomology ring of the symmetric square of quaternionic projective space, which has been an open problem since computations with symmetric squares were first proposed in the 1930's. The geometry of this particular case forms an essential part of the thesis, and unexpected results concerning two universal Pin(4) bundles are also included. The cohomological computations involve a commutative ladder of long exact sequences, which arise by decomposing the symmetric square and the corresponding Borel space in compatible ways. The geometry

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Kakuhama, Hirotaka. "FORMAL DEGREES AND LOCAL THETA CORRESPONDENCE: QUATERNIONIC CASE." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263429.

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Melo, Thiago de. "Torção de Reidemeister das formas espaciais esféricas." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-26052009-135508/.

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Neste trabalho, estudamos a ação dos grupos dos quatérnios generalizados \'Q IND.4t\', nas esferas, com o objetivo de calcularmos a torção de Reidemeister dos espaços quocientes, chamados de Formas Espaciais Esféricas Quaterniônicas. Calculamos a torção de Ray-Singer das esferas, dos espaços lenticulares e do cone sobre as esferas, este último fornecendo o caso particular do disco, usando a base para a homologia definida em [27]. Para as variedades fechadas, obtivemos a torção analítica por meio do Teorema de Cheeger-Müller [7, 22], e para o disco, por meio de uma fórmula provada por Brüning e

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Dufour, Quentin. "Une construction de métriques quaternion-kählériennes à partir du groupe G2." Thesis, Paris 6, 2014. http://www.theses.fr/2014PA066142/document.

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Le théorème central de cette thèse est une construction de métriques quaternion-kählériennes sur des variétés de dimension 8 modelées sur l'espace symétrique de type non-compact G2/SO(4). Cette construction s'inscrit dans la lignée des constructions de LeBrun (1989) et de Biquard (2000) pour lesquelles d'un côté les variétés quaternion-kählériennes construites possèdent un modèle homogène qui est un espace symétrique de type non-compact G/K, et d'un autre côté, les données initiales peuvent s'interpréter comme étant des déformations d'un bord de Furstenberg G/P où P est un sous-groupe paraboli

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Suzuki, Miyu. "Quaternion distinguished representations and unstable base change for unitary groups." Kyoto University, 2020. http://hdl.handle.net/2433/253065.

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Philippe, Zoe. "Invariants globaux des variétés hyperboliques quaterioniques." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0453/document.

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Dans une première partie de cette thèse, nous donnons des minorations universelles ne dépendant que de la dimension – explicites, de trois invariants globaux des quotients des espaces hyperboliques quaternioniques : leur rayon maximal, leur volume, ainsi que leur caractéristique d’Euler. Nous donnons également une majoration de leur constante de Margulis, montrant que celle-ci décroit au moins comme une puissance négative de la dimension. Dans une seconde partie, nous étudions un réseau remarquable des isométries du plan hyperbolique quaternionique, le groupe modulaire d’Hurwitz. Nous montrons

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Hopkinson, Jeremy Franklin Lawrence. "Quoric manifolds." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/quoric-manifolds(e2ba0b95-ea55-4cb7-a98e-4f7426ce52cd).html.

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Davis and Januszkiewicz introduced in 1981 a family of compact real manifolds, the Quasi-Toric Manifolds, with a group action by a torus, a direct product of circle (T) groups. Their manifolds have an orbit space which is a simple polytope with a distinct isotropy subgroup associated to each face of the polytope, subject to some consistency conditions. They defined a characteristic function which captured the properties of the isotropy subgroups, and showed that their manifolds can be classified by the polytope and characteristic function. They further showed that the cohomology ring of the ma

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Meinke, Benedict [Verfasser], and Suárez Vicente [Akademischer Betreuer] Cortés. "Homogeneous almost hypercomplex and almost quaternionic pseudo-Hermitian manifolds with irreducible isotropy groups / Benedict Meinke. Betreuer: Vicente Cortés Suárez." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2016. http://d-nb.info/108176810X/34.

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Meinke, Benedict Verfasser], and Vicente [Akademischer Betreuer] [Cortés. "Homogeneous almost hypercomplex and almost quaternionic pseudo-Hermitian manifolds with irreducible isotropy groups / Benedict Meinke. Betreuer: Vicente Cortés Suárez." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2016. http://d-nb.info/108176810X/34.

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Reynolds, Paul. "On conformal submersions and manifolds with exceptional structure groups." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/6218.

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This thesis comes in three main parts. In the first of these (comprising chapters 2 - 6), the basic theory of Riemannian and conformal submersions is described and the relevant geometric machinery explained. The necessary Clifford algebra is established and applied to understand the relationship between the spinor bundles of the base, the fibres and the total space of a submersion. O'Neill-type formulae relating the covariant derivatives of spinor fields on the base and fibres to the corresponding spinor field on the total space are derived. From these, formulae for the Dirac operators are obt

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Books on the topic "Quaternionic group"

1

Ivanov, Stefan P. Quaternionic contact: Einstein structures and the quaternionic contact yamabe problems. American Mathematical Society, 2014.

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Ivanov, Stefan P. Extremals for the Sobolev inequality and the quaternionic contact Yamabe problem. World Scientific, 2011.

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Rotations, quaternions, and double groups. Dover Publications, 2005.

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Rotations, quaternions, and double groups. Clarendon Press, 1986.

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Conformal groups in geometry and spin structures. Birkhauser, Boston, 2008.

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Quaternions, Clifford Algebras and Relativistic Physics. Birkhäuser Basel, 2007.

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7

Vidonne. Groupe circulaire rotations et quaternions capes et agregation de mathematiques. Ellipses Marketing, 2001.

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8

Roberts, Brooks Keiluweit. Lifting of automorphic forms on the units of a quaternion algebra to automorphic forms on the symplectic groups. 1992.

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9

M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Residually Pseudo-Split Buildings. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0033.

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This chapter presents results about a residually pseudo-split Bruhat-Tits building Ξ‎L. It begins with a case for some quadratic space of type E⁶, E₇, and E₈ in order to identify an unramified extension such that the residue field is a pseudo-splitting field. It then considers a wild quaternion or octonion division algebra and the existence of an unramified quadratic extension L/K such that L is a splitting field of the quaternion division algebra. It also discusses the properties of an unramified extension L/K and shows that every exceptional Bruhat-Tits building is the fixed point building o

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M¨uhlherr, Bernhard, Holger P. Petersson, and Richard M. Weiss. Strictly Semi-linear Automorphisms. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691166902.003.0030.

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This chapter considers the action of a strictly semi-linear automorphism fixing a root on the corresponding root group. It begins with the hypothesis whereby Δ‎ is a Moufang spherical building and Π‎ is the Coxeter diagram of Δ‎; here the chapter fixes an apartment Σ‎ of Δ‎ and a root α‎ of Σ‎. The discussion then turns to a number of assumptions about an isomorphism of Moufang sets, anisotropic quadratic space, and root group sequence, followed by a lemma where E is an octonion division algebra with center F and norm N and D is a quaternion subalgebra of E. The chapter concludes with three ve

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Book chapters on the topic "Quaternionic group"

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Matheus Silva Santos, Carlos. "An Example of Quaternionic Kontsevich-Zorich Monodromy Group." In Dynamical Aspects of Teichmüller Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92159-4_6.

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Colombo, Fabrizio, and Jonathan Gantner. "Perturbations of the generator of a group." In Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16409-6_5.

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Baker, Andrew. "Algebras, Quaternions and Quaternionic Symplectic Groups." In Springer Undergraduate Mathematics Series. Springer London, 2002. http://dx.doi.org/10.1007/978-1-4471-0183-3_4.

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Baldi, Annalisa, Bruno Franchi, and Francesca Tripaldi. "Gagliardo-Nirenberg Inequalities for Horizontal Vector Fields in the Engel Group and in the Seven-Dimensional Quaternionic Heisenberg Group." In Geometric Methods in PDE’s. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-02666-4_16.

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Johnson, F. E. A. "Group Rings of Quaternion Groups." In Syzygies and Homotopy Theory. Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2294-4_12.

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Voight, John. "Quaternionic arithmetic groups." In Graduate Texts in Mathematics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-56694-4_38.

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Miyake, Toshitsune. "Unit Groups of Quaternion Algebras." In Springer Monographs in Mathematics. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-29593-3_5.

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Binz, Ernst, and Sonja Pods. "The skew field of quaternions." In The Geometry of Heisenberg Groups. American Mathematical Society, 2008. http://dx.doi.org/10.1090/surv/151/01.

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Zhu, Guangyu, Shuicheng Yan, Tony X. Han, and Changsheng Xu. "Generative Group Activity Analysis with Quaternion Descriptor." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17829-0_1.

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Girard, Patrick R. "Quaternions, Clifford Algebra and Symmetry Groups." In Applications of Geometric Algebra in Computer Science and Engineering. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0089-5_27.

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Conference papers on the topic "Quaternionic group"

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SCOLARICI, G., and L. SOLOMBRINO. "QUATERNIONIC GROUP REPRESENTATIONS AND THEIR CLASSIFICATIONS." In Proceedings of the Second Meeting. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810038_0024.

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Terze, Zdravko, Andreas Mueller, and Dario Zlatar. "Redundancy-Free Integration of Rotational Quaternions in Minimal Form." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35118.

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Redundancy-free computational procedure for solving dynamics of rigid body by using quaternions as the rotational kinematic parameters will be presented in the paper. On the contrary to the standard algorithm that is based on redundant DAE-formulation of rotational dynamics of rigid body that includes algebraic equation of quaternions’ unit-length that has to be solved during marching-in-time, the proposed method will be based on the integration of a local rotational vector in the minimal form at the Lie-algebra level of the SO(3) rotational group during every integration step. After local rot

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Purwar, Anurag, and Q. J. Ge. "Polar Decomposition of Unit Dual Quaternions." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70882.

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This paper seeks to extend the notion of polar decomposition from matrix algebra to dual quaternion algebra. The goal is to obtain a simple, efficient and explicit method for determining the polar decompositions (PD) of spatial displacements in Euclidean three-space that belong to a special Euclidean Group known as SE(3). It has been known that such a decomposition is equivalent to the projection of an element of SE(3) onto SO(4) that yields hyper spherical displacements that best approximate rigid-body displacements. It is shown in this paper that a dual quaternion representing an element of

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Müller, Andreas, Zdravko Terze, and Viktor Pandza. "A Non-Redundant Formulation for the Dynamics Simulation of Multibody Systems in Terms of Unit Dual Quaternions." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60191.

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Quaternions are favorable parameters to describe spatial rotations of rigid bodies since they give rise to simple equations governing the kinematics and attitude dynamics in terms of simple algebraic equations. Dual quaternions are the natural extension to rigid body motions. They provide a singularity-free purely algebraic parameterization of rigid body motions, and thus serve as global parameters within the so-called absolute coordinate formulation of MBS. This attractive feature is owed to the inherent redundancy of these parameters since they must satisfy two quadratic conditions (unit con

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Deveci, Ömür, and Abdulkadir Kalemci. "The Lehmer lengths of the generalized quaternion group Q2n." In II. INTERNATIONAL CONFERENCE ON ADVANCES IN NATURAL AND APPLIED SCIENCES: ICANAS 2017. Author(s), 2017. http://dx.doi.org/10.1063/1.4981650.

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Dapeng, Han, Wei Qing, and Li Zexiang. "Attitude Control Based on the Lie-group Structure of Unit Quaternions." In 2007 Chinese Control Conference. IEEE, 2006. http://dx.doi.org/10.1109/chicc.2006.4347101.

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KOCA, MEHMET, and N. ÖZDEŞ KOCA. "COXETER GROUPS, QUATERNIONS, SYMMETRIES OF POLYHEDRA AND 4D POLYTOPES." In Proceedings of the 13th Regional Conference. World Scientific Publishing Company, 2012. http://dx.doi.org/10.1142/9789814417532_0003.

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Colón, Diego. "Cartan’s Connection, Fiber Bundles and Quaternions in Kinematics and Dynamics Calculations." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46758.

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It is used the concept of Cartan’s connection and principal fiber bundles to obtain formulas for kinematics and dynamics calculations for robotic manipulators. A principal fiber bundle is a differentiable manifold formed by a base space B (in this case ℝ3)) plus all possible reference frames attached to a point p ∈ B (that is the fiber Sp). Cartan’s connections are the most general way to represent velocity of frames. In previous works, those ideas were applied to fiber bundles with fibers homomorphic to the Lie group SO(3) (or SE(3)). In this paper, it is applied to the case of fibers homomor

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Lopes Vieira, Vandenberg, Reginaldo Palazzo, and Mercio Botelho Faria. "On the arithmetic Fuchsian groups derived from quaternion orders." In 2006 International Telecommunications Symposium. IEEE, 2006. http://dx.doi.org/10.1109/its.2006.4433342.

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Zhang, Xuan, Shaofei Qin, Yi Xu, and Hongteng Xu. "Quaternion Product Units for Deep Learning on 3D Rotation Groups." In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2020. http://dx.doi.org/10.1109/cvpr42600.2020.00733.

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