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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2017: 1.49

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1435-5345
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Volume 2012, Issue 665

Issues

Hochschild and cyclic homology of Yang–Mills algebras

Estanislao Herscovich
  • Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, 1428, Buenos Aires, Argentina
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/ Andrea Solotar
  • Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, 1428, Buenos Aires, Argentina
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Published Online: 2011-06-28 | DOI: https://doi.org/10.1515/CRELLE.2011.107

Abstract

The aim of this article is to present a detailed algebraic computation of the Hochschild and cyclic homology groups of the Yang–Mills algebras YM(n) (n ∈ ℕ≧2) defined by A. Connes and M. Dubois-Violette in [8], continuing thus the study of these algebras that we have initiated in [17]. The computation involves the use of a spectral sequence associated to the natural filtration on the universal enveloping algebra YM(n) provided by a Lie ideal 𝔱𝔶𝔪(n) in 𝔶𝔪(n) which is free as Lie algebra. As a corollary, we describe the Lie structure of the first Hochschild cohomology group.

About the article

Received: 2009-07-27

Revised: 2010-09-28

Published Online: 2011-06-28

Published in Print: 2012-04-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2012, Issue 665, Pages 73–156, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2011.107.

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