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DUALITIES FOR MAXIMAL COACTIONS
- Source :
- Journal of the Australian Mathematical Society. 102:224-254
- Publication Year :
- 2016
- Publisher :
- Cambridge University Press (CUP), 2016.
-
Abstract
- We present a new construction of crossed-product duality for maximal coactions that uses Fischer's work on maximalizations. Given a group $G$ and a coaction $(A,\delta)$ we define a generalized fixed-point algebra as a certain subalgebra of $M(A\rtimes_{\delta} G \rtimes_{\widehat{\delta}} G)$, 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 $C^*$-correspondences. Also, we outline partial results for the "outer" category, studied previously by the authors.<br />Comment: Minor revision
- Subjects :
- Mathematics::Operator Algebras
Group (mathematics)
General Mathematics
010102 general mathematics
Subalgebra
Mathematics - Operator Algebras
Duality (optimization)
Context (language use)
46L55 (Primary), 46M15 (Secondary)
01 natural sciences
Unicode
Action (physics)
Combinatorics
Crossed product
Mathematics::Quantum Algebra
0103 physical sciences
FOS: Mathematics
Homomorphism
010307 mathematical physics
0101 mathematics
Operator Algebras (math.OA)
Mathematics
Subjects
Details
- ISSN :
- 14468107 and 14467887
- Volume :
- 102
- Database :
- OpenAIRE
- Journal :
- Journal of the Australian Mathematical Society
- Accession number :
- edsair.doi.dedup.....e54319b13f55e10eed0009f6ea85a60c