Hochschild homology and the second obstruction for pseudoisotopy

Dennis, R. Keith; Igusa, Kiyoshi

doi:10.1007/bfb0062165

Cited by 23 publications

(17 citation statements)

References 7 publications

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“…One recovers the explicit maps given in [28] for this situation, and hence from Theorem 4.5 the classical result [28,12] of Morita invariance in Hochschild theory follows. In case M = R, with [24,Prop.…”

Section: Morita Invariance Of Cyclicsupporting

confidence: 76%

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Morita Base Change in Hopf-Cyclic (Co)Homology

Kaoutit

Kowalzig

2012

Lett Math Phys

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ABSTRACT. In this paper, we establish the invariance of cyclic (co)homology of left Hopf algebroids under the change of Morita equivalent base algebras. The classical result on Morita invariance for cyclic homology of associative algebras appears as a special example of this theory. In our main application we consider the Morita equivalence between the algebra of complex-valued smooth functions on the classical 2-torus and the coordinate algebra of the noncommutative 2-torus with rational parameter. We then construct a Morita base change left Hopf algebroid over this noncommutative 2-torus and show that its cyclic (co)homology can be computed by means of the homology of the Lie algebroid of vector fields on the classical 2-torus.

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Section: Morita Invariance Of Cyclicsupporting

confidence: 76%

“…As an application, we first indicate how the classical result of Morita invariance for cyclic homology of associative algebras (see, e.g., [7,12,28]) fits into our general theory.…”

Section: Introductionmentioning

confidence: 99%

Morita Base Change in Hopf-Cyclic (Co)Homology

Kaoutit

Kowalzig

2012

Lett Math Phys

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“…The notation in 1.2.2 is motivated by the classical fact that In fact, we know that "trace" induces isomorphisms in Hochschild homology [DI,3.7], as well as in HC [LQ,1.7], HP and HC~ [G, 1.3.8]. EXAMPLE 1.3.2.…”

Section: Cyclic Modulesmentioning

confidence: 99%

Nil 𝐾-theory maps to cyclic homology

Weibel¹

1987

Trans. Amer. Math. Soc.

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Algebraic K K -theory breaks into two pieces: nil K K -theory and Karoubi-Villamayor K K -theory. Karoubi has constructed Chern classes from the latter groups into cyclic homology. We construct maps from nil K K -theory to cyclic homology which are compatible with Karoubi’s maps, but with a degree shift. Several recent results show that in characteristic zero our map is often an isomorphism.

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“…One of the basic features of Hochschild (co-)homology is its invariance under derived equivalence, see [25], in particular, it is invariant under Morita equivalence, a result originally established by Dennis-Igusa [18], see also [26]. This raises the question how Hochschild cohomology compares in general for algebras that are just ingredients of a Morita context.…”

Section: Introductionmentioning

confidence: 99%

Morita contexts, idempotents, and Hochschild cohomology—with applications to invariant rings

Buchweitz¹

2003

Commutative Algebra

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Abstract. We investigate how to compare Hochschild cohomology of algebras related by a Morita context. Interpreting a Morita context as a ring with distinguished idempotent, the key ingredient for such a comparison is shown to be the grade of the Morita defect, the quotient of the ring modulo the ideal generated by the idempotent. Along the way, we show that the grade of the stable endomorphism ring as a module over the endomorphism ring controls vanishing of higher groups of selfextensions, and explain the relation to various forms of the Generalized Nakayama Conjecture for Noetherian algebras. As applications of our approach we explore to what extent Hochschild cohomology of an invariant ring coincides with the invariants of the Hochschild cohomology.

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Hochschild homology and the second obstruction for pseudoisotopy

Cited by 23 publications

References 7 publications

Morita Base Change in Hopf-Cyclic (Co)Homology

Morita Base Change in Hopf-Cyclic (Co)Homology

Nil 𝐾-theory maps to cyclic homology

Morita contexts, idempotents, and Hochschild cohomology—with applications to invariant rings

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