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Generalized permutative representations of Cuntz algebras

Research paper by Katsunori Kawamura

Indexed on: 23 Mar '06Published on: 23 Mar '06Published in: Mathematics - Operator Algebras



Abstract

We introduce representations of the Cuntz algebra $\con$ which are parameterized by sequences in the set of unit vectors in ${\bf C}^{N}$. These representations are natural generalizations of permutative representations by Bratteli-Jorgensen and Davidson-Pitts. We show their existence, irreducibility, equivalence, uniqueness of irreducible decomposition and decomposition formulae by using parameters of representations.