Note on Morita Equivalence in Ring Extensions

Yamanaka, Satoshi

doi:10.1080/00927872.2015.1044098

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…Therefore A and B are Morita equivalent if and only if they are Morita isomorphic. About applications of Morita equivalence, see [2,43].…”

Section: General Formulasmentioning

confidence: 99%

Morita isomorphism for Cuntz algebras

Kawamura¹

2020

Preprint

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Let Rep On denote the category of all nondegenerate * representations of the Cuntz algebra On. For any 2 ≤ n, m < ∞, we construct an isomorphism functor Fn,m from Rep Om to Rep On such that (i) Fn,m commutes with infinite direct sum, (ii) Fn,m • F m,l = F n,l and Fm,n = F −1 n,m for any 2 ≤ n, m, l < ∞, (iii) for the von Neumann algebra Nπ generated by the image of a representation π, N Fn,m(π) and Nπ are isomorphic for any π in Rep Om, and (iv) there exists a functor F∞,n from Rep On to Rep O∞ with a right inverse such that F∞,n • Fn,m = F∞,m for any 2 ≤ n, m < ∞.

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“…Therefore A and B are Morita equivalent if and only if they are Morita isomorphic. About applications of Morita equivalence, see [2,43].…”

Section: General Formulasmentioning

confidence: 99%

Morita isomorphism for Cuntz algebras

Kawamura¹

2020

Preprint

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“…The condition that the rectangle above commutes applied to R ∈ R M becomes B Q ⊗ S R ∼ = B P , also valid as B-R-bimodules due to naturality, noted as an equivalent condition in the proposition below. The proposition below characterizes Morita equivalence of ring extensions in many equivalent ways, condition (2) being the definition in [38,21,48]. (6) the following rectangle, with sides representing the induction functors, commutes up to a natural isomorphism,…”

Section: Morita Equivalent Ring Extensionsmentioning

confidence: 99%

“…In this section we continue a study of Morita equivalence of ring extensions in [38,21,48], though with an emphasis on functors and categories. We will briefly provide the classical background theory, and prove that depth, relative cyclic homology as well as the bipartite graphs of a semisimple complex subalgebra pair are all Morita invariant properties of a ring or algebra extension.…”

Section: Morita Equivalent Ring Extensionsmentioning

confidence: 99%

Algebra depth in tensor categories

Kadison¹

2016

Bull. Belg. Math. Soc. Simon Stevin

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Study of the quotient module of a finite-dimensional Hopf subalgebra pair in order to compute its depth yields a relative Maschke Theorem, in which semisimple extension is characterized as being separable, and is therefore an ordinary Frobenius extension. We study the core Hopf ideal of a Hopf subalgebra, noting that the length of the annihilator chain of tensor powers of the quotient module is linearly related to the depth, if the Hopf algebra is semisimple. A tensor categorical definition of depth is introduced, and a summary from this new point of view of previous results are included. It is shown in a last section that the depth, Bratteli diagram and relative cyclic homology of algebra extensions are Morita invariants.1991 Mathematics Subject Classification. 16D20, 16D90, 16T05, 18D10, 20C05.

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Morita Isomorphism for Cuntz Algebras

Kawamura

2022

Algebr Represent Theor

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Note on Morita Equivalence in Ring Extensions

Cited by 3 publications

References 9 publications

Morita isomorphism for Cuntz algebras

Morita isomorphism for Cuntz algebras

Algebra depth in tensor categories

Morita Isomorphism for Cuntz Algebras

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