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The BV-algebra structure of the Hochschild cohomology of the group ring of cyclic groups of prime order. (English) Zbl 1370.16006

Cano, Leonardo (ed.) et al., Geometric, algebraic and topological methods for quantum field theory. Proceedings of the 8th Villa de Leyva summer school, Villa de Leyva, Colombia, July 15–27, 2013. Hackensack, NJ: World Scientific (ISBN 978-981-4730-87-7/hbk; 978-981-4730-89-1/ebook). 353-372 (2017).
Summary: We construct a different Batalin-Vilkovisky algebra structure on the Hochschild cohomology of the algebra of truncated polynomials with coefficients in a field of \(p\) elements with \(p\) prime. We accomplish this by transfering the Frobenius form of the group ring of cyclic groups. We also explicitly calculate the Batalin-Vilkovisky algebra structure of the Hochschild cohomology of the group rings of cyclic groups of prime order. The algebra structure, even the Gesterhaber structure has been calculated before, but the BV structure that we calculate is a new one.
For the entire collection see [Zbl 1364.81010].

MSC:

16E40 (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.)
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
16S34 Group rings
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