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Algebras and Representation Theory

, Volume 21, Issue 1, pp 61–86 | Cite as

Gerstenhaber Algebra Structure on the Hochschild Cohomology of Quadratic String Algebras

  • María Julia RedondoEmail author
  • Lucrecia Román
Article

Abstract

We describe the Gerstenhaber algebra structure on the Hochschild cohomology HH(A) when A is a quadratic string algebra. First we compute the Hochschild cohomology groups using Barzdell’s resolution and we describe generators of these groups. Then we construct comparison morphisms between the bar resolution and Bardzell’s resolution in order to get formulae for the cup product and the Lie bracket. We find conditions on the bound quiver associated to string algebras in order to get non-trivial structures.

Keywords

Hochschild cohomology Cup product Lie bracket String algebras 

Mathematics Subject Classification (2010)

16E40 16W99 

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Notes

Acknowledgments

The first author is a researcher and the second author has a fellowship from CONICET, Argentina. This work has been supported by the project PICT-2011-1510.

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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Instituto de Matemática (INMABB), Departamento de MatemáticaUniversidad Nacional del Sur (UNS)-CONICETBahía BlancaArgentina

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