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 (Formula presented.) and a coaction (Formula presented.) we define a generalized fixed-point algebra as a certain subalgebra of (Formula presented.), 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 (Formula presented.)-correspondences. Also, we outline partial results for the ‘outer’ category, which has been studied previously by the authors.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalJournal of the Australian Mathematical Society
DOIs
StateAccepted/In press - May 12 2016

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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