Dialgebra cohomology as a G-algebra

Majumdar, Anita; Mukherjee, Goutam

doi:10.1090/S0002-9947-03-03387-7

Dialgebra cohomology as a G-algebra
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by Anita Majumdar and Goutam Mukherjee

Trans. Amer. Math. Soc. 356 (2004), 2443-2457

DOI: https://doi.org/10.1090/S0002-9947-03-03387-7

Published electronically: November 25, 2003

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Abstract:

It is well known that the Hochschild cohomology $H^*(A,A)$ of an associative algebra $A$ admits a G-algebra structure. In this paper we show that the dialgebra cohomology $HY^*(D,D)$ of an associative dialgebra $D$ has a similar structure, which is induced from a homotopy G-algebra structure on the dialgebra cochain complex $CY^*(D,D)$.

References

Alessandra Frabetti, Dialgebra (co)homology with coefficients, Dialgebras and related operads, Lecture Notes in Math., vol. 1763, Springer, Berlin, 2001, pp. 67–103. MR 1860995, DOI 10.1007/3-540-45328-8_{3}
Murray Gerstenhaber, The cohomology structure of an associative ring, Ann. of Math. (2) 78 (1963), 267–288. MR 161898, DOI 10.2307/1970343
Murray Gerstenhaber and Alexander A. Voronov, Homotopy $G$-algebras and moduli space operad, Internat. Math. Res. Notices 3 (1995), 141–153. MR 1321701, DOI 10.1155/S1073792895000110
Ginot, G. Homology et modèle minimal des algèbres de Gerstenhaber, preprint 2002, http://www-irma.u-strasbg.fr/ ̃ginot/gerstenhaber.ps.
Victor Ginzburg and Mikhail Kapranov, Koszul duality for operads, Duke Math. J. 76 (1994), no. 1, 203–272. MR 1301191, DOI 10.1215/S0012-7094-94-07608-4
Jean-Louis Loday, Dialgebras, Dialgebras and related operads, Lecture Notes in Math., vol. 1763, Springer, Berlin, 2001, pp. 7–66. MR 1860994, DOI 10.1007/3-540-45328-8_{2}
Majumdar, A. and Mukherjee, G. Deformation theory of dialgebras, K-theory 27 (2002), 33-60.
J. P. May, Definitions: operads, algebras and modules, Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995) Contemp. Math., vol. 202, Amer. Math. Soc., Providence, RI, 1997, pp. 1–7. MR 1436912, DOI 10.1090/conm/202/02587