The Experts below are selected from a list of 15396 Experts worldwide ranked by ideXlab platform
A I Shtern - One of the best experts on this subject based on the ideXlab platform.
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stable pseudorepresentations of a Connected Lie Group
2019Co-Authors: A I ShternAbstract:The class of the so-called stable pseudorepresentations of Groups is introduced, general properties of this class are indicated, and it is shown that every finite-dimensional locally bounded quasirepresentation of a Connected Lie Group can be approximated by a stable pseudorepresentation which is automatically continuous on the commutator subGroup of the Group.
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continuity criterion for the restriction to the commutator subGroup of a locally bounded finite dimensional representation of a Connected Lie Group
2019Co-Authors: A I ShternAbstract:We prove that a locally bounded finite-dimensional representation of a Connected Lie Group has a continuous restriction with respect to the original topology of the Group to the commutator subGroup of the Group if and only if the restriction of the representation to the center of a Levi subGroup is continuous with respect to the original topology of the Group.
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hochschild kernel for locally bounded finite dimensional representations of a Connected Lie Group
2011Co-Authors: A I ShternAbstract:Abstract A direct version of Hochschild’s description of the universal representation kernel for continuous linear finite-dimensional representations of Connected Lie Groups is presented and used to describe the intersection of kernels of locally bounded (not necessarily continuous) linear representations of a given Connected Lie Group.
Lauret, Emilio A. - One of the best experts on this subject based on the ideXlab platform.
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Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie Groups
2021Co-Authors: Lauret, Emilio A.Abstract:Let $G$ be a compact Connected Lie Group of dimension $m$. Once a bi-invariant metric on $G$ is fixed, left-invariant metrics on $G$ are in correspondence with $m\times m$ positive definite symmetric matrices. We estimate the diameter and the smallest positive eigenvalue of the Laplace-Beltrami operator associated to a left-invariant metric on $G$ in terms of the eigenvalues of the corresponding positive definite symmetric matrix. As a consequence, we give partial answers to a conjecture by Eldredge, Gordina and Saloff-Coste; namely, we give large subsets $\mathcal S$ of the space of left-invariant metrics $\mathcal M$ on $G$ such that there exists a positive real number $C$ depending on $G$ and $\mathcal S$ such that $\lambda_1(G,g)\operatorname{diam}(G,g)^2\leq C$ for all $g\in\mathcal S$. The existence of the constant $C$ for $\mathcal S=\mathcal M$ is the original conjecture.Comment: Subsections 3.3 and 4.3 have been drastically modifie
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Diameter and Laplace eigenvalue estimates for compact homogeneous Riemannian manifolds
2021Co-Authors: Lauret, Emilio A.Abstract:Let $G$ be a compact Connected Lie Group and let $K$ be a closed subGroup of $G$. In this paper we study whether the functional $g\mapsto \lambda_1(G/K,g)\operatorname{diam}(G/K,g)^2$ is bounded among $G$-invariant metrics $g$ on $G/K$. Eldredge, Gordina, and Saloff-Coste conjectured in 2018 that this assertion holds when $K$ is trivial; the only particular cases known so far are when $G$ is abelian, $\operatorname{SU}(2)$, and $\operatorname{SO}(3)$. In this article we prove the existence of the mentioned upper bound for every compact homogeneous space $G/K$ having multiplicity-free isotropy representation.Comment: Accepted for publication in Transformation Groups. arXiv admin note: text overlap with arXiv:2004.0035
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Diameter and Laplace eigenvalue estimates for left-invariant metrics on compact Lie Groups
2020Co-Authors: Lauret, Emilio A.Abstract:Let $G$ be a compact Connected Lie Group of dimension $m$. Once a bi-invariant metric on $G$ is fixed, left-invariant metrics on $G$ are in correspondence with $m\times m$ positive definite symmetric matrices. We estimate the diameter and the smallest positive eigenvalue of the Laplace-Beltrami operator associated to a left-invariant metric on $G$ in terms of the eigenvalues of the corresponding positive definite symmetric matrix. As a consequence, we give partial answers to a conjecture by Eldredge, Gordina and Saloff-Coste; namely, we give large subsets $\mathcal S$ of the space of left-invariant metrics $\mathcal M$ on $G$ such that there exists a positive real number $C$ depending on $G$ and $\mathcal S$ such that $\lambda_1(G,g)\operatorname{diam}(G,g)^2\leq C$ for all $g\in\mathcal S$. The existence of the constant $C$ for $\mathcal S=\mathcal M$ is the original conjecture
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Diameter and Laplace eigenvalue estimates for compact homogeneous Riemannian manifolds
2020Co-Authors: Lauret, Emilio A.Abstract:Let $G$ be a compact Connected Lie Group and let $K$ be a closed subGroup of $G$. In this paper we study whether the functional $g\mapsto \lambda_1(G/K,g)\operatorname{diam}(G/K,g)^2$ is bounded by above among $G$-invariant metrics $g$ on $G/K$. Eldredge, Gordina, and Saloff-Coste conjectured in 2018 that this assertion holds when $K$ is trivial; the only particular cases known so far are when $G$ is abelian, $\operatorname{SU}(2)$, and $\operatorname{SO}(3)$. In this article we prove the existence of the mentioned upper bound for every compact homogeneous space $G/K$ having multiplicity-free isotropy representation.Comment: arXiv admin note: text overlap with arXiv:2004.0035
Bruce Gilligan - One of the best experts on this subject based on the ideXlab platform.
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complexifying Lie Group actions on homogeneous manifolds of non compact dimension two
2014Co-Authors: Ruhallah S Ahmadi, Bruce GilliganAbstract:If X is a Connected complex manifold with dX = 2 that admits the holomorphic and transitive action of a (Connected) Lie Group G, then the action extends to an action of the complexification b G of G on X except when either the unit disk or else a strictly pseudoconcave homogeneous complex manifold is involved as base or fiber in some homogeneous fibration of X.
Szabo, Richard J. - One of the best experts on this subject based on the ideXlab platform.
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Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
2021Co-Authors: Bunk Severin, Müller Lukas, Szabo, Richard J.Abstract:We study bundle gerbes on manifolds $M$ that carry an action of a Connected Lie Group $G$. We show that these data give rise to a smooth 2-Group extension of $G$ by the smooth 2-Group of hermitean line bundles on $M$. This 2-Group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-Group extension in terms of a homotopy-coherent version of the associated bundle construction. We apply our results to give new descriptions of nonassociative magnetic translations in quantum mechanics and the Faddeev-Mickelsson-Shatashvili anomaly in quantum field theory. We also propose a definition of smooth string 2-Group models within our geometric framework. Starting from a basic gerbe on a compact simply-Connected Lie Group $G$, we prove that the smooth 2-Group extensions of $G$ arising from our construction provide new models for the string Group of $G$.Comment: 79 pages, 2 figures; v2: minor corrections, comments and references added; Final version to be published in Communications in Mathematical Physic
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Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
2020Co-Authors: Bunk Severin, Müller Lukas, Szabo, Richard J.Abstract:We study bundle gerbes on manifolds $M$ that carry an action of a Connected Lie Group $G$. We show that these data give rise to a smooth 2-Group extension of $G$ by the smooth 2-Group of hermitean line bundles on $M$. This 2-Group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-Group extension in terms of a homotopy-coherent version of the associated bundle construction. We apply our results to give new descriptions of nonassociative magnetic translations in quantum mechanics and the Faddeev-Mickelsson-Shatashvili anomaly in quantum field theory. We also propose a definition of smooth string 2-Group models within our geometric framework. Starting from a basic gerbe on a compact simply-Connected Lie Group $G$, we prove that the smooth 2-Group extensions of $G$ arising from our construction provide new models for the string Group of $G$.Comment: 78 pages, 2 figure
Ruhallah S Ahmadi - One of the best experts on this subject based on the ideXlab platform.
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complexifying Lie Group actions on homogeneous manifolds of non compact dimension two
2014Co-Authors: Ruhallah S Ahmadi, Bruce GilliganAbstract:If X is a Connected complex manifold with dX = 2 that admits the holomorphic and transitive action of a (Connected) Lie Group G, then the action extends to an action of the complexification b G of G on X except when either the unit disk or else a strictly pseudoconcave homogeneous complex manifold is involved as base or fiber in some homogeneous fibration of X.
