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G-structure on the cohomology of Hopf algebras


Authors: Marco A. Farinati and Andrea L. Solotar
Journal: Proc. Amer. Math. Soc. 132 (2004), 2859-2865
MSC (2000): Primary 16E40, 16W30
DOI: https://doi.org/10.1090/S0002-9939-04-07274-0
Published electronically: June 2, 2004
MathSciNet review: 2063104
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Abstract: We prove that $\mathrm{Ext} ^{\bullet}_A(k,k)$ is a Gerstenhaber algebra, where $A$ is a Hopf algebra. In case $A=D(H)$ is the Drinfeld double of a finite-dimensional Hopf algebra $H$, our results imply the existence of a Gerstenhaber bracket on $H^{\bullet}_{GS}(H,H)$. This fact was conjectured by R. Taillefer. The method consists of identifying $H^{\bullet}_{GS}(H,H)\cong {\mathrm{Ext}}^{\bullet}_A(k,k)$ as a Gerstenhaber subalgebra of $H^{\bullet}(A,A)$ (the Hochschild cohomology of $A$).


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Additional Information

Marco A. Farinati
Affiliation: Departamento de Matemática Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria Pab I. 1428, Buenos Aires, Argentina
Email: mfarinat@dm.uba.ar

Andrea L. Solotar
Affiliation: Departamento de Matemática Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria Pab I. 1428, Buenos Aires, Argentina
Email: asolotar@dm.uba.ar

DOI: https://doi.org/10.1090/S0002-9939-04-07274-0
Keywords: Gerstenhaber algebras, Hopf algebras, Hochschild cohomology
Received by editor(s): August 27, 2002
Received by editor(s) in revised form: March 19, 2003
Published electronically: June 2, 2004
Additional Notes: This research was partially supported by UBACYT X062 and Fundación Antorchas (proyecto 14022 - 47). Both authors are research members of CONICET (Argentina).
Communicated by: Martin Lorenz
Article copyright: © Copyright 2004 American Mathematical Society

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