The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products

Thomas Tradler[1]

  • [1] Thomas Tradler College of Technology of the City University of New York Department of Mathematics 300 Jay Street Brooklyn NY 11201 (USA)

Annales de l’institut Fourier (2008)

  • Volume: 58, Issue: 7, page 2351-2379
  • ISSN: 0373-0956

Abstract

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We define a BV-structure on the Hochschild cohomology of a unital, associative algebra A with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomology of a unital A ∞ -algebra with a symmetric and non-degenerate ∞ -inner product.

How to cite

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Tradler, Thomas. "The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products." Annales de l’institut Fourier 58.7 (2008): 2351-2379. <http://eudml.org/doc/10381>.

@article{Tradler2008,
abstract = {We define a BV-structure on the Hochschild cohomology of a unital, associative algebra $A$ with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomology of a unital $A_\infty $-algebra with a symmetric and non-degenerate $\infty $-inner product.},
affiliation = {Thomas Tradler College of Technology of the City University of New York Department of Mathematics 300 Jay Street Brooklyn NY 11201 (USA)},
author = {Tradler, Thomas},
journal = {Annales de l’institut Fourier},
keywords = {Hochschild cohomology; Batalin Vilkovisky algebra; Gerstenhaber structures; BV structures; Batalin-Vilkovisky algebras; inner products},
language = {eng},
number = {7},
pages = {2351-2379},
publisher = {Association des Annales de l’institut Fourier},
title = {The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products},
url = {http://eudml.org/doc/10381},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Tradler, Thomas
TI - The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products
JO - Annales de l’institut Fourier
PY - 2008
PB - Association des Annales de l’institut Fourier
VL - 58
IS - 7
SP - 2351
EP - 2379
AB - We define a BV-structure on the Hochschild cohomology of a unital, associative algebra $A$ with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomology of a unital $A_\infty $-algebra with a symmetric and non-degenerate $\infty $-inner product.
LA - eng
KW - Hochschild cohomology; Batalin Vilkovisky algebra; Gerstenhaber structures; BV structures; Batalin-Vilkovisky algebras; inner products
UR - http://eudml.org/doc/10381
ER -

References

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