English

Crossed Products by Endomorphisms, Vector Bundles and Group Duality

Operator Algebras 2011-11-21 v4 Category Theory K-Theory and Homology

Abstract

We construct the crossed product of a C(X)-algebra by an endomorphism, in such a way that the endomorphism itself becomes induced by the bimodule of continuous sections of a vector bundle. Some motivating examples for such a construction are given. Furthermore, we study the C*-algebra of G-invariant elements of the Cuntz-Pimsner algebra associated with a G-vector bundle, where G is a (noncompact, in general) group. In particular, the C*-algebra of invariant elements w.r.t. the action of the group of special unitaries of the given vector bundle is a crossed product in the above sense. We also study the analogous construction on certain Hilbert bimodules, called 'noncommutative pullbacks'.

Keywords

Cite

@article{arxiv.math/0301214,
  title  = {Crossed Products by Endomorphisms, Vector Bundles and Group Duality},
  author = {Ezio Vasselli},
  journal= {arXiv preprint arXiv:math/0301214},
  year   = {2011}
}

Comments

37 pages, uses xy. Revised version of the first part of the previous submission, to appear on Int. J. Math

R2 v1 2026-07-22T16:51:16.560Z