Geodesic
Gerstenhaber structure on Hochschild cohomology of the Fomin–Kirillov algebra on 3 generators
Documenta mathematica, Tome 27 (2022), pp. 1773-1804

Voir la notice de l'article provenant de la source EMS Press

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 
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
@article{10_4171_dm_x18,
     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/}
}
TY  - JOUR
AU  - Ziling Li
AU  - Estanislao Herscovich
TI  - Gerstenhaber structure on Hochschild cohomology of the Fomin–Kirillov algebra on 3 generators
JO  - Documenta mathematica
PY  - 2022
SP  - 1773
EP  - 1804
VL  - 27
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/x18/
DO  - 10.4171/dm/x18
ID  - 10_4171_dm_x18
ER  - 
%0 Journal Article
%A Ziling Li
%A Estanislao Herscovich
%T Gerstenhaber structure on Hochschild cohomology of the Fomin–Kirillov algebra on 3 generators
%J Documenta mathematica
%D 2022
%P 1773-1804
%V 27
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/x18/
%R 10.4171/dm/x18
%F 10_4171_dm_x18

Cité par Sources :