DUALITIES for MAXIMAL COACTIONS

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2 Scopus citations

Abstract

We present a new construction of crossed-product duality for maximal coactions that uses Fischer's work on maximalizations. Given a group and a coaction we define a generalized fixed-point algebra as a certain subalgebra of , and recover the coaction via this double crossed product. Our goal is to formulate this duality in a category-theoretic context, and one advantage of our construction is that it breaks down into parts that are easy to handle in this regard. We first explain this for the category of nondegenerate∗-homomorphisms and then, analogously, for the category of -correspondences. Also, we outline partial results for the 'outer' category, which has been studied previously by the authors.

Original languageEnglish (US)
Pages (from-to)224-254
Number of pages31
JournalJournal of the Australian Mathematical Society
Volume102
Issue number2
DOIs
StatePublished - Apr 1 2017

Keywords

  • C -correspondence
  • action
  • category equivalence
  • coaction
  • crossed-product duality
  • exterior equivalence
  • outer conjugacy

ASJC Scopus subject areas

  • Mathematics(all)

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