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Related papers: Cartan decomposition for complex loop groups

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We classify compact manifolds of dimension three equipped with a path structure and a fixed contact form (which we refer to as a strict path structure) under the hypothesis that their automorphism group is non-compact. We use a Cartan…

Differential Geometry · Mathematics 2023-03-09 Elisha Falbel , Martin Mion-Mouton , Jose Miguel Veloso

The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification,…

Differential Geometry · Mathematics 2011-04-07 Akihiro Nishio , Osami Yasukura

A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum groups, we…

High Energy Physics - Theory · Physics 2008-02-03 Peter Schupp , Paul Watts , Bruno Zumino

We show that compact complex manifolds of algebraic dimension zero bearing a holomorphic Cartan geometry of algebraic type have infinite fundamental group. This generalizes the main Theorem in [DM] where the same result was proved for the…

Differential Geometry · Mathematics 2019-12-03 Indranil Biswas , Sorin Dumitrescu , Benjamin McKay

We describe invariant principal and Cartan connections on homogeneous principal bundles and show how to calculate the curvature and the holonomy; in the case of an invariant Cartan connection we give a formula for the infinitesimal…

Differential Geometry · Mathematics 2011-05-27 Matthias Hammerl

We prove a uniform version of Varadhan decomposition for shift-invariant closed uniform forms associated to large scale interacting systems on general crystal lattices. In particular, this result includes the case of translation invariant…

Probability · Mathematics 2022-09-01 Kenichi Bannai , Makiko Sasada

We construct a one parameter deformation of the group of $2\times 2$ upper triangular matrices with determinant 1 using the twisting construction. An interesting feature of this new example of a locally compact quantum group is that the…

Operator Algebras · Mathematics 2008-01-15 Pierre Fima , Leonid Vainerman

We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…

Quantum Algebra · Mathematics 2020-03-12 Julien Bichon , Maeva Paradis

We give a geometric method for determining the cohomology groups of a polyhedral product under suitable freeness conditions or with coefficients taken in a field. This is done by considering first the special case for which the pairs of…

Algebraic Topology · Mathematics 2023-05-24 A. Bahri , M. Bendersky , F. R. Cohen , S. Gitler

We relate a Chaplygin type system to a Cartan decomposition of a real semi-simple Lie group. The resulting system is described in terms of the structure theory associated to the Cartan decomposition. It is shown to possess a preserved…

Differential Geometry · Mathematics 2009-07-06 Simon Hochgerner

This article makes the key observation that when using cylindrical algebraic decomposition (CAD) to solve a problem with respect to a set of polynomials, it is not always the signs of those polynomials that are of paramount importance but…

Symbolic Computation · Computer Science 2013-07-10 Russell Bradford , James H. Davenport , Matthew England , Scott McCallum , David Wilson

We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…

Group Theory · Mathematics 2015-08-27 Attila Egri-Nagy , Chrystopher L. Nehaniv

In this paper, we introduce the Newton decomposition on a connected reductive $p$-adic group $G$. Based on it we give a nice decomposition of the cocenter of its Hecke algebra. Here we consider both the ordinary cocenter associated to the…

Representation Theory · Mathematics 2018-03-09 Xuhua He

A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found that can be approximated by…

High Energy Physics - Theory · Physics 2009-10-28 Robert J. Perry

A scheme to perform the Cartan decomposition for the Lie algebra su(N) of arbitrary finite dimensions is introduced. The schme is based on two algebraic structures, the conjugate partition and the quotient algebra, that are easily generated…

Quantum Physics · Physics 2007-05-23 Zheng-Yao Su

This paper analyses the finer structure of Newton strata in loop groups. These can be decomposed into so-called central leaves. We define them, and determine their global geometric structure. We then study the closure of central leaves,…

Algebraic Geometry · Mathematics 2016-07-01 Eva Viehmann , Han Wu

We analyze the h-deformations of the Lorentz group and their associated spacetimes. We prove that they have a twisted character and give explicitly the twisting matrices. After studying the representations of one of the deformed spacetime…

q-alg · Mathematics 2011-07-26 J. A. de Azcárraga , P. P. Kulish , F. Rodenas

We investigate the relation between Cartan decompositions of the unitary group and discrete quantum symmetries. To every Cartan decomposition there corresponds a quantum symmetry which is the identity when applied twice. As an application,…

Quantum Physics · Physics 2007-05-23 Domenico D'Alessandro , Francesca Albertini

We present a procedure which enables the computation and the description of structures of isotropy subgroups of the group of complex orthogonal matrices with respect to the action of *congruence on Hermitian matrices. A key ingredient in…

Differential Geometry · Mathematics 2023-05-24 Tadej Starčič

The purpose of this paper is to apply deformation quantization to the study of the coadjoint orbit method in the case of real reductive groups. We first prove some general results on the existence of equivariant deformation quantization of…

Representation Theory · Mathematics 2018-09-25 Naichung Conan Leung , Shilin Yu