NDLI: Representations of Currents Taking Values in a Totally Disconnected Group

Content Provider	Springer Nature Link
Author	Kuhn, M. Gabriella
Copyright Year	2010
Abstract	Let $G={\mathcal{A}ut(\mathcal{T})}$ be the group of all automorphisms of a homogeneous tree $\mathcal{T}$ of degree q + 1 ≥ 3 and (X, m) a compact metrizable measure space with a probability measure m. We assume that μ has no atoms. The group $\mathcal{G}={\mathcal{A}ut(\mathcal{T})}^X=G^X$ of bounded measurable currents is the completion of the group of step functions $f:X\to{\mathcal{A}ut(\mathcal{T})}$ with respect to a suitable metric. Continuos functions form a dense subgroup of $\mathcal{G}$ . Following the ideas of I.M. Gelfand, M.I. Graev and A.M. Vershik we shall construct an irreducible family of representations of $\mathcal{G}$ . The existence of such representations depends deeply from the nonvanisching of the first cohomology group $H^1({\mathcal{A}ut(\mathcal{T})},\pi)$ for a suitable infinite dimensional π.
Ending Page	730
Page Count	20
Starting Page	711
File Format	PDF
ISSN	1386923X
e-ISSN	15729079
Journal	Algebras and Representation Theory
Issue Number	4
Volume Number	14
Language	English
Publisher	Springer Netherlands
Publisher Date	2010-08-03
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Associative Rings and Algebras Homogeneous tree Positive definite functions on groups, semigroups, etc. Representations of Lie and linear algebraic groups over real fields: analytic methods Tensor product Non-associative Rings and Algebras Groups as automorphisms of other structures Commutative Rings and Algebras Spherical representations Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $W$ -algebras and other current algebras and their representations Cocycle Continuous cohomology
Content Type	Text
Resource Type	Article
Subject	Mathematics

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