Results 41 to 50 of about 3,483,162 (228)
On extensions of representations for compact Lie groups
Journal of Pure and Applied Algebra, 2003 Let $H$ be a closed normal subgroup of a compact Lie group $G$ such that $G/H$ is connected. This paper provides a necessary and sufficient condition for every complex representation of $H$ to be extendible to $G$, and also for every complex $G$-vector bundle over the homogeneous space $G/H$ to be trivial.
Cho, JH, Kim, MK, Suh, DY Suh, Dong Youp
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Hom-Lie Algebras and Hom-Lie Groups, Integration and Differentiation [PDF]
SIGMA 16 (2020), 137, 22 pages, 2019 In this paper, we introduce the notion of a (regular) Hom-Lie group. We associate a Hom-Lie algebra to a Hom-Lie group and show that every regular Hom-Lie algebra is integrable. Then, we define a Hom-exponential (Hexp) map from the Hom-Lie algebra of a Hom-Lie group to the Hom-Lie group and discuss the universality of this Hexp map.
arxiv +1 more source
Spiders for rank 2 Lie algebras
, 1996 A spider is an axiomatization of the representation theory of a group, quantum group, Lie algebra, or other group or group-like object. We define certain combinatorial spiders by generators and relations that are isomorphic to the representation theories
A.A. Kirillov +13 more
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Spinor symmetries and underlying properties
European Physical Journal C: Particles and Fields, 2020 By exploring a spinor space whose elements carry a spin 1/2 representation of the Lorentz group and satisfy the the Fierz–Pauli–Kofink identities we show that certain symmetries operations form a Lie group.
J. M. Hoff da Silva +3 more
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Vacuum polarization of scalar field on Lie groups with Bi-invariant metric [PDF]
Компьютерные исследования и моделирование, 2015 We consider vacuum polarization of a scalar field on the Lie groups with a bi-invariant metric of Robertson-Walker type. Using the method of orbits we found expression for the vacuum expectation values of the energy-momentum tensor of the scalar field ...
Alexander Igorevich Breev +1 more
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Entropy, 2016 We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical ...
Frédéric Barbaresco
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Distribution representations of Lie groups
Journal of Mathematical Analysis and Applications, 1978 We study representations of Lie groups in Banach spaces, particularly distribution representations (or smeared representations) and differentiable representations. These objects, which we define, are shown to be natural and useful generalizations of the classical unitary representations and the point strong operator continuous representations.
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Integration of semidirect product Lie 2-algebras
, 2012 The semidirect product of a Lie algebra and a 2-term representation up to homotopy is a Lie 2-algebra. Such Lie 2-algebras include many examples arising from the Courant algebroid appearing in generalized complex geometry.
Sheng, Yunhe, Zhu, Chenchang
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Lie cohomology of representations of nilpotent Lie groups and holomorphically induced representations [PDF]
Transactions of the American Mathematical Society, 1980 Let U be a locally injective, Moore-Wolf square integrable representa- tion of a nilpotent Lie group N. Let (%, X) be a complex, maximal subordinate pair corresponding to U and let 5Q, = ker X n 3C. The space C°°(U) of differentiable vectors for U is an 3Q module. In this work we compute the Lie algebra cohomology HiCXq, C°°(U)) of this Lie module.
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Rationality of representations of linear Lie groups [PDF]
Proceedings of the American Mathematical Society, 1992 We are concerned with real linear Lie groups G G having the property that every finite-dimensional continuous representation of G G is rational.
Dong Hoon Lee, Ta Sun Wu
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