Illinois Journal of Mathematics

Symmetry in tensor algebras over Hilbert space

Palle E. T. Jorgensen and Ilwoo Cho

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This paper deals with three issues: (1) Unitary representations $U$ of a scale of (finite and infinite dimensional) non-compact Lie groups $G(H)$ built on a fixed complex Hilbert space $H$; and their covariant systems. Our computations for these representations make use of the associated Lie algebras. (2) The covariant representations involve the $C^{*}$-algebras going by the names, the Toeplitz algebras, and the Cuntz algebras. (3) An essential result which also is used throughout is our computation of the commutant of the unitary representation $U$ of $G(H)$ mentioned in (1). For a fixed Hilbert space $H$, we apportion the commutant as a specific projective limit-algebra of operators.

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Illinois J. Math., Volume 55, Number 3 (2011), 977-1013.

First available in Project Euclid: 29 May 2013

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Primary: 05E18: Group actions on combinatorial structures 11F70: Representation-theoretic methods; automorphic representations over local and global fields 37C45: Dimension theory of dynamical systems 37C80: Symmetries, equivariant dynamical systems 46L54: Free probability and free operator algebras 47L30: Abstract operator algebras on Hilbert spaces 47L90: Applications of operator algebras to physics


Jorgensen, Palle E. T.; Cho, Ilwoo. Symmetry in tensor algebras over Hilbert space. Illinois J. Math. 55 (2011), no. 3, 977--1013. doi:10.1215/ijm/1369841794.

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