Results 1 to 10 of about 1,026,898 (347)

Inexistence de pavages mesurables invariants par un réseau dans un espace homogène d'un groupe de Lie simple [PDF]

arXiv, 2022
We prove that an homogeneous space of an almost simple Lie group does not have any measurable tiling invariant by a lattice of the Lie group. This refines the Howe-Moore ergodicity theorem. -- On d\'emontre qu'un espace homog\`ene d'un groupe de Lie presque simple n'admet pas de pavage mesurable invariant par un r\'eseau du groupe de Lie.
arxiv  

η and λ deformations as E-models

Nuclear Physics B, 2015
We show that the so-called λ deformed σ-model as well as the η deformed one belong to a class of the E-models introduced in the context of the Poisson–Lie-T-duality. The λ and η theories differ solely by the choice of the Drinfeld double; for the λ model
Ctirad Klimčík
doaj   +1 more source

Derivation double Lie algebras [PDF]

arXiv, 2014
We study classical R-matrices D for Lie algebras L such that D is also a derivation of L. This yields derivation double Lie algebras (L,D). The motivation comes from recent work on post-Lie algebra structures on pairs of Lie algebras arising in the study of nil-affine actions of Lie groups. We prove that there are no nontrivial simple derivation double
arxiv  

Involutive representations of coordinate algebras and quantum spaces

Journal of High Energy Physics, 2017
We show that s u 2 $$ \mathfrak{s}\mathfrak{u}(2) $$ Lie algebras of coordinate operators related to quantum spaces with s u 2 $$ \mathfrak{s}\mathfrak{u}(2) $$ noncommutativity can be conveniently represented by SO(3)-covariant poly-differential ...
Tajron Jurić, Timothé Poulain, Jean-Christophe Wallet   +2 more
doaj   +1 more source

On the Third-Degree Continuous Cohomology of Simple Lie Groups [PDF]

J. Lie Theory 29 (2019), no. 4, 1007-1016, 2018
We show that the class of connected, simple Lie groups that have non-vanishing third-degree continuous cohomology with trivial $\mathbb{R}$-coefficients consists precisely of all simple complex Lie groups and of $\widetilde{\mathrm{SL}_2(\mathbb{R})}$.
arxiv  

Finite simple groups of Lie type as expanders

Journal of the European Mathematical Society, 2011
We prove that all finite simple groups of Lie type, with the exception of the Suzuki groups, can be made into a family of expanders in a uniform way. This confirms a conjecture of Babai, Kantor and Lubotzky from 1989, which has already been proved by Kassabov for sufficiently large rank.
openaire   +4 more sources

Fusion Systems and Rank $2$ Simple Groups of Lie Type

Forum of Mathematics, Sigma
For any prime p and S a p-group isomorphic to a Sylow p-subgroup of a rank $2$ simple group of Lie type in characteristic p, we determine all saturated fusion systems supported on S up to isomorphism.
Martin van Beek
doaj   +1 more source

Poisson-Lie duals of the η deformed symmetric space sigma model

Journal of High Energy Physics, 2017
Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model.
Ben Hoare, Fiona K. Seibold
doaj   +1 more source

Maximal abelian subgroups of compact simple Lie groups [PDF]

arXiv, 2012
We classify abelian subgroups of the automorphism group of any compact simple Lie algebra whose centralizer has the same dimension as the dimension of the subgroup. This leads to a classification of the maximal abelian subgroups of compact simple groups of adjoint type and a classification of the fine group gradings of complex simple Lie algebras.
arxiv  

Local Second Order Sobolev Regularity for p-Laplacian Equation in Semi-Simple Lie Group

Mathematics
In this paper, we establish a structural inequality of the ∞-subLaplacian ▵0,∞ in a class of the semi-simple Lie group endowed with the horizontal vector fields X1,…,X2n.
Chengwei Yu, Yue Zeng
doaj   +1 more source