Cohomology of Yang-Mills algebras

Michael Movshev

doi:10.4171/JNCG/24

Cohomology of Yang-Mills algebras

Michael Movshev

Mathematics

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

3 Scopus citations

Abstract

In this paper we compute cyclic and Hochschild homology of the universal envelope U(YM) of the Yang-Mills Lie algebra YM. We also compute Hochschild cohomology with coefficients in U(YM), considered as a bimodule over itself. The result of the calculations depends on the number of generators n of YM. The semidirect product SD(n) × Cⁿ acts by derivations upon U(YM). One of the important consequences of our results is that if n ≥ 3 then the Lie algebra of outer derivations of U(YM) coincides with SD(n) × C ⁿ.

Original language	English
Pages (from-to)	353-404
Number of pages	52
Journal	Journal of Noncommutative Geometry
Volume	2
Issue number	3
DOIs	https://doi.org/10.4171/JNCG/24
State	Published - 2008

Keywords

Cohomology
Derivations
Yang-Mills algebra

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10.4171/JNCG/24

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title = "Cohomology of Yang-Mills algebras",

abstract = "In this paper we compute cyclic and Hochschild homology of the universal envelope U(YM) of the Yang-Mills Lie algebra YM. We also compute Hochschild cohomology with coefficients in U(YM), considered as a bimodule over itself. The result of the calculations depends on the number of generators n of YM. The semidirect product SD(n) × Cn acts by derivations upon U(YM). One of the important consequences of our results is that if n ≥ 3 then the Lie algebra of outer derivations of U(YM) coincides with SD(n) × C n.",

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author = "Michael Movshev",

year = "2008",

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journal = "Journal of Noncommutative Geometry",

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AU - Movshev, Michael

PY - 2008

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N2 - In this paper we compute cyclic and Hochschild homology of the universal envelope U(YM) of the Yang-Mills Lie algebra YM. We also compute Hochschild cohomology with coefficients in U(YM), considered as a bimodule over itself. The result of the calculations depends on the number of generators n of YM. The semidirect product SD(n) × Cn acts by derivations upon U(YM). One of the important consequences of our results is that if n ≥ 3 then the Lie algebra of outer derivations of U(YM) coincides with SD(n) × C n.

AB - In this paper we compute cyclic and Hochschild homology of the universal envelope U(YM) of the Yang-Mills Lie algebra YM. We also compute Hochschild cohomology with coefficients in U(YM), considered as a bimodule over itself. The result of the calculations depends on the number of generators n of YM. The semidirect product SD(n) × Cn acts by derivations upon U(YM). One of the important consequences of our results is that if n ≥ 3 then the Lie algebra of outer derivations of U(YM) coincides with SD(n) × C n.

KW - Cohomology

KW - Derivations

KW - Yang-Mills algebra

UR - https://www.scopus.com/pages/publications/80053644244

U2 - 10.4171/JNCG/24

DO - 10.4171/JNCG/24

M3 - Article

AN - SCOPUS:80053644244

SN - 1661-6952

VL - 2

SP - 353

EP - 404

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

IS - 3

ER -

Cohomology of Yang-Mills algebras

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