Crossed products by abelian semigroups via transfer operators

Details Crossed products by abelian semigroups via transfer operators Crossed products by abelian semigroups via transfer operators

2005-02-15

arxiv.org/abs/math/0502307v1

Mathematics

Operator Algebras

19 pages

Scientific paper

We propose a generalisation of Exel's crossed product by a single endomorphism and a transfer operator to the case of actions of abelian semigroups of endomorphisms and associated transfer operators. The motivating example for our definition yields new crossed products, not obviously covered by familiar theory. Our technical machinery builds on Fowler's theory of Toeplitz and Cuntz-Pimsner algebras of discrete product systems of Hilbert bimodules, which we need to expand to cover a natural notion of relative Cuntz-Pimsner algebras of product systems.

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