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IRREDUCIBLE REPRESENTATIONS OF C*-CROSSED PRODUCTS BY FINITE GROUPS
 

Summary: IRREDUCIBLE REPRESENTATIONS OF C*-CROSSED
PRODUCTS BY FINITE GROUPS
ALVARO ARIAS AND FRŽEDŽERIC LATRŽEMOLI`ERE
Abstract. We describe the structure of the irreducible represen-
tations of crossed products of unital C*-algebras by actions of finite
groups in terms of irreducible representations of the C*-algebras
on which the groups act. We then apply this description to derive a
characterization of irreducible representations of crossed-products
by finite cyclic groups in terms of representations of the C*-algebra
and its fixed point subalgebra. These results are applied to crossed-
products by the permutation group on three elements and illus-
trated by various examples.
1. Introduction
What is the structure of irreducible representations of C*-crossed-
products A G of an action of a finite group G on a unital C*-
algebra A? Actions by finite groups provide interesting examples, such
as quantum spheres [1, 2] and actions on the free group C*-algebras
[3], among many examples, and have interesting general properties, as
those found for instance in [9]. Thus, understanding the irreducible
representations of their crossed-products is a natural inquiry, which we

  

Source: Arias, Alvaro - Department of Mathematics, University of Denver

 

Collections: Mathematics