logo CRAS
Comptes Rendus. Mathématique
Algèbre
BD algebras and group cohomology
Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 925-937.

BD algebras (Beilinson–Drinfeld algebras) are algebraic structures which are defined similarly to BV algebras (Batalin–Vilkovisky algebras). The equation defining the BD operator has the same structure as the equation for BV algebras, but the BD operator is increasing with degree +1. We obtain methods of constructing BD algebras in the context of group cohomology.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/crmath.246
Classification : 20J06,  16E40,  16E45
Constantin-Cosmin Todea 1

1. Department of Mathematics, Technical University of Cluj-Napoca, Str. G. Baritiu 25, Cluj-Napoca 400027, Romania
@article{CRMATH_2021__359_8_925_0,
     author = {Constantin-Cosmin Todea},
     title = {BD algebras and group cohomology},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {925--937},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {8},
     year = {2021},
     doi = {10.5802/crmath.246},
     language = {en},
}
TY  - JOUR
AU  - Constantin-Cosmin Todea
TI  - BD algebras and group cohomology
JO  - Comptes Rendus. Mathématique
PY  - 2021
DA  - 2021///
SP  - 925
EP  - 937
VL  - 359
IS  - 8
PB  - Académie des sciences, Paris
UR  - https://doi.org/10.5802/crmath.246
DO  - 10.5802/crmath.246
LA  - en
ID  - CRMATH_2021__359_8_925_0
ER  - 
%0 Journal Article
%A Constantin-Cosmin Todea
%T BD algebras and group cohomology
%J Comptes Rendus. Mathématique
%D 2021
%P 925-937
%V 359
%N 8
%I Académie des sciences, Paris
%U https://doi.org/10.5802/crmath.246
%R 10.5802/crmath.246
%G en
%F CRMATH_2021__359_8_925_0
Constantin-Cosmin Todea. BD algebras and group cohomology. Comptes Rendus. Mathématique, Tome 359 (2021) no. 8, pp. 925-937. doi : 10.5802/crmath.246. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.246/

[1] Andrés Angel; Diego Duarte The BV-algebra structure of the Hochschild cohomology of the group ring of cyclic groups of prime order, Geometric, algebraic and topological methods for quantum field theory, World Scientific, 2017, pp. 353-372 | Zbl 1370.16006

[2] David J. Benson Representations and cohomology II: Cohomology of groups and modules, Cambridge Studies in Advanced Mathematics, 31, Cambridge University Press, 1991 | Zbl 0731.20001

[3] David J. Benson; Radha Kessar; Markus Linckelmann On the BV structure of the Hochschild cohomology of finite group algebras https://arxiv.org/abs/2005.01694

[4] Alberto S. Cattaneo; Domenico Fiorenza; Riccardo Longoni Graded Poisson algebras, Encyclopedia of Mathematical Physics, Elsevier, 2006, pp. 560-567 | Article

[5] Claude Cibils; Andrea Solotar Hochschild cohomology algebra of abelian groups, Arch. Math., Volume 68 (1997) no. 1, pp. 17-21 | Article | MR 1421841 | Zbl 0872.16004

[6] Kevin Costello; Owen Gwilliam Factorization algebras in quantum field theory, Volume 1, New Mathematical Monographs, 31, Cambridge University Press, 2016 | Zbl 1377.81004

[7] Murray Gerstenhaber The cohomology structure of an associative ring, Ann. Math., Volume 78 (1963), pp. 267-288 | Article | MR 161898

[8] Ezra Getzler Batalin–Vilkovisky algebra and two dimensional topological fields theory, Commun. Math. Phys., Volume 159 (1994), pp. 265-285 | Article

[9] Yuming Liu; Guodong Zhou The Batalin–Vilkovisky structure over the Hochschild cohomology ring of a group algebra, J. Noncommut. Geom., Volume 10 (2016) no. 3, pp. 811-858 | MR 3554837 | Zbl 1376.16008

[10] nLab authors Relation between BV and BD https://ncatlab.org/nlab/show/relation+between+BV+and+BD (accessed April 2021)

[11] Thomas Tradler The Batalin–Vilkovisky algebra on Hochschild cohomology induced by infinity inner products, Ann. Inst. Fourier, Volume 58 (2008) no. 7, pp. 2351-2379 | Article | Numdam | MR 2498354 | Zbl 1218.16004

Cité par Sources :