Geodesic
Gerstenhaber structure on Hochschild cohomology of the Fomin–Kirillov algebra on 3 generators
Documenta mathematica, Tome 27 (2022), pp. 1773-1804 Cet article a éte moissonné depuis la source EMS Press

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The goal of this article is to compute the Gerstenhaber bracket of the Hochschild cohomology of the Fomin–Kirillov algebra on three generators over a field of characteristic different from 2 and 3. This is in part based on a general method we introduce to easily compute the Gerstenhaber bracket between elements of HH0(A) and elements of HHn(A) for n∈N0​, the method by M. Suárez-Álvarez [J. Pure Appl. Algebra 221, No. 8, 1981–1998 (2017; Zbl 1392.16009)] to calculate the Gerstenhaber bracket between elements of HH1(A) and elements of HHn(A) for any n∈N0​, as well as an elementary result that allows to compute the remaining brackets from the previous ones. We also show that the Gerstenhaber bracket of HH∙(A) is not induced by any Batalin–Vilkovisky generator.
DOI : 10.4171/dm/x18
Classification : 16E40, 16S37, 18G10
Mots-clés : Hochschild cohomology, Fomin-Kirillov algebra, Gerstenhaber bracket 
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     author = {Ziling Li and Estanislao Herscovich},
     title = {Gerstenhaber structure on {Hochschild} cohomology of the {Fomin{\textendash}Kirillov} algebra on 3 generators},
     journal = {Documenta mathematica},
     pages = {1773--1804},
     year = {2022},
     volume = {27},
     doi = {10.4171/dm/x18},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x18/}
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Ziling Li; Estanislao Herscovich. Gerstenhaber structure on Hochschild cohomology of the Fomin–Kirillov algebra on 3 generators. Documenta mathematica, Tome 27 (2022), pp. 1773-1804. doi: 10.4171/dm/x18

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