Formality theorems for hochschild complexes and their applications

Vasiliy Dolgushev; Dmitry Tamarkin; Boris Tsygan

doi:10.1007/s11005-009-0350-3

Formality theorems for hochschild complexes and their applications

Vasiliy Dolgushev^*, Dmitry Tamarkin, Boris Tsygan

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.

Original language	English (US)
Pages (from-to)	103-136
Number of pages	34
Journal	Letters in Mathematical Physics
Volume	90
Issue number	1
DOIs	https://doi.org/10.1007/s11005-009-0350-3
State	Published - Nov 2009

Funding

We would like to thank J. Stasheff for discussions and for his useful comments on the first version of our manuscript. D.T. and B.T. are supported by NSF grants. The work of V.D. is partially supported by the Grant for Support of Scientific Schools NSh-3036.2008.2.

Keywords

Deformation quantization
Hochschild complexes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-009-0350-3

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title = "Formality theorems for hochschild complexes and their applications",

abstract = "We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.",

keywords = "Deformation quantization, Hochschild complexes",

author = "Vasiliy Dolgushev and Dmitry Tamarkin and Boris Tsygan",

note = "Funding Information: We would like to thank J. Stasheff for discussions and for his useful comments on the first version of our manuscript. D.T. and B.T. are supported by NSF grants. The work of V.D. is partially supported by the Grant for Support of Scientific Schools NSh-3036.2008.2.",

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AU - Dolgushev, Vasiliy

AU - Tamarkin, Dmitry

AU - Tsygan, Boris

N1 - Funding Information: We would like to thank J. Stasheff for discussions and for his useful comments on the first version of our manuscript. D.T. and B.T. are supported by NSF grants. The work of V.D. is partially supported by the Grant for Support of Scientific Schools NSh-3036.2008.2.

PY - 2009/11

Y1 - 2009/11

N2 - We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.

AB - We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.

KW - Deformation quantization

KW - Hochschild complexes

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Formality theorems for hochschild complexes and their applications

Abstract

Funding

Keywords

ASJC Scopus subject areas

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