Discrete Inclusions of C-algebras

Discrete Inclusions of C-algebras

We introduce the category of C*-discrete inclusions of C*-algebras \(A\subset B\) with a faithful conditional expectation \(E:B\twoheadrightarrow A\). This class includes many examples such as finite Watatani index inclusions, and also abundant infinite index inclusions like crossed products by oute...

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Veröffentlicht in:arXiv.org 2024-08
Hauptverfasser: Roberto Hernández Palomares, Nelson, Brent
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Sprache:eng
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Algebra
Group theory
Inclusions
Invariants
Lattices (mathematics)
Mathematical analysis
Tensors
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description We introduce the category of C*-discrete inclusions of C*-algebras \(A\subset B\) with a faithful conditional expectation \(E:B\twoheadrightarrow A\). This class includes many examples such as finite Watatani index inclusions, and also abundant infinite index inclusions like crossed products by outer actions of discrete (quantum) groups and unitary tensor categories. We prove irreducible \((A'\cap B= \mathbb{C}1)\) C*-discrete inclusions are precisely crossed products by outer actions of unitary tensor categories and certain C*-algebra objects.
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subjects Algebra
Group theory
Inclusions
Invariants
Lattices (mathematics)
Mathematical analysis
Tensors
title Discrete Inclusions of C-algebras
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