A little bit of extra functoriality for Ext and the computation of the Gerstenhaber bracket

We show that the action of the Lie algebra HH1(A) of outer derivations of an associative algebra A on the Hochschild cohomology HH•(A) of A given by the Gerstenhaber bracket can be computed in terms of an arbitrary projective resolution of A as an A-bimodule, without having recourse to comparison ma...

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Autor principal: Suárez-Álvarez, M.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Elsevier B.V. 2017
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245 1 2 |a A little bit of extra functoriality for Ext and the computation of the Gerstenhaber bracket 
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504 |a Bardzell, M.J., The alternating syzygy behavior of monomial algebras (1997) J. Algebra, 188 (1), pp. 69-89. , MR1432347 
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504 |a Farinati, M., Hochschild duality, localization, and smash products (2005) J. Algebra, 284 (1), pp. 415-434. , MR2115022 
504 |a Gerstenhaber, M., The cohomology structure of an associative ring (1963) Ann. Math. (2), 78, pp. 267-288. , MR0161898 
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504 |a Negron, C., Alternate Approaches to the Cup Product and Gerstenhaber Bracket on Hochschild Cohomology (2015), Ph.D. thesis University of Washington Seattle, WA, United States MR3438933; Negron, C., Witherspoon, S., An alternate approach to the Lie bracket on Hochschild cohomology (2015), http://arxiv.org/abs/1406.0036v3; Retakh, V.S., Homotopy properties of categories of extensions (1986) Usp. Mat. Nauk, 41 (6(252)), pp. 179-180. , MR890505 
504 |a Román, L., La cohomología de Hochschild de álgebras de cuerdas y su estructura de álgebra de Gerstenhaber (2016), Ph.D. thesis Universidad Nacional del Sur, Bahía Blanca Argentina; Shepler, A.V., Witherspoon, S., Hochschild cohomology and graded Hecke algebras (2008) Trans. Am. Math. Soc., 360 (8), pp. 3975-4005. , MR2395161 
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504 |a Schwede, S., An exact sequence interpretation of the Lie bracket in Hochschild cohomology (1998) J. Reine Angew. Math., 498, pp. 153-172. , MR1629858 
504 |a Sköldberg, E., A contracting homotopy for Bardzell's resolution (2008) Math. Proc. R. Ir. Acad., 108 (2), pp. 111-117. , MR2475805 
504 |a Xu, Y.-G., Han, Y., Jiang, W.-F., Hochschild cohomology of truncated quiver algebras (2007) Sci. China Ser. A, 50 (5), pp. 727-736. , MR2355359 
520 3 |a We show that the action of the Lie algebra HH1(A) of outer derivations of an associative algebra A on the Hochschild cohomology HH•(A) of A given by the Gerstenhaber bracket can be computed in terms of an arbitrary projective resolution of A as an A-bimodule, without having recourse to comparison maps between the resolution and the bar resolution. © 2016 Elsevier B.V.  |l eng 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428) Ciudad de Buenos Aires, Argentina 
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