Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We study homological properties of a family of algebras called toupie algebras. Our main objective is to obtain the Gerstenhaber structure of their Hochschild cohomology, with the purpose of describing the Lie algebra structure of the first Hochschild cohomology space, together with the Lie module structure of the whole Hochschild cohomology. © 2019, Springer Nature B.V.

Registro:

Documento: Artículo
Título:Gerstenhaber Structure on Hochschild Cohomology of Toupie Algebras
Autor:Artenstein, D.; Lanzilotta, M.; Solotar, A.
Filiación:Instituto de Matemática y Estadística “Rafael Laguardia”, Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, Montevideo, Uruguay
IMAS and Dto. de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón 1, Buenos Aires, 1428, Argentina
Palabras clave:Gerstenhaber algebra; Hochschild cohomology; Topology; Cohomology; Lie Algebra; Module structure; Algebra
Año:2019
DOI: http://dx.doi.org/10.1007/s10468-019-09854-y
Título revista:Algebras and Representation Theory
Título revista abreviado:Algebr Represent Theory
ISSN:1386923X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1386923X_v_n_p_Artenstein

Referencias:

  • Artenstein, D., (2015) Cohomología De Hochschild Y Estructura De Gerstenhaber De Las álgebras Toupie, Universidad De La República, , http://www.cmat.edu.uy/cmat/biblioteca/documentos/tesis/tesis-de-doctorado/phdthesisreference.2016-05-03.1935241415
  • Artenstein, D., (2011) Clasificación De Álgebras Toupie, Universidad De La República, , http://www.cmat.edu.uy/cmat/biblioteca/documentos/tesis/maestria/pdfs
  • Barot, M., Kussin, D., Lenzing, H., Extremal properties for concealed-canonical algebras (2013) Colloq. Math., 130 (2), pp. 183-219
  • Bustamante, J.C., The cohomology structure of string algebras (2006) J. Pure Appl. Algebra, 204, pp. 616-626
  • Castonguay, D., Dionne, J., Huard, F., Lanzilotta, M., Toupie Algebras, Some Examples of Laura Algebras
  • Cibils, C., Rigidity of truncated quiver algebras (1990) Adv. Math., 79, pp. 18-42
  • Chouhy, S., Solotar, A., Projective resolutions of associative algebras and ambiguities (2015) J. Algebra, 432, pp. 22-61
  • Fulton, W., Harris, J., Representation theory: a first course (1991) Grad. Texts Math., 129, p. XV, 551
  • Gatica, A., Lanzilotta, M., Hochschild cohomology of a generalization of canonical algebras (2010) São Paulo J. Math. Sci., 2, pp. 251-271
  • Green, E., Schroll, S., Multiserial and special multiserial algebras and their representations (2016) Adv. Math., 302, pp. 1111-1136
  • Gerstenhaber, M., Schack, S.D., Relative Hochschild cohomology rigid algebras, and the Bockstein (1986) J. Pure Appl. Algebra, 43 (1), pp. 53-74
  • Humphreys, J.E., (1972) Introduction to Lie Algebras and Representation Theory. Graduate Texts in Mathematics, vol. 9, , Springer, Berlin
  • Lenzing, H., de la Peña, J.A., Concealed-canonical algebras and separating tubular families (1999) Proc. London Math. Soc. (3), 78 (3), pp. 513-540
  • Redondo, M.J., Román, L., Gerstenhaber algebra structure on the Hochschild cohomology of quadratic string algebras (2018) Algebr. Represent. Theory, 21 (1), pp. 61-86
  • Redondo, M.J., Román, L., Hochschild cohomology of triangular string algebras and its ring structure (2014) J. Pure Appl. Algebra, 218 (5), pp. 925-936
  • Ringel, C.M., (1984) Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math, 1099. , Springer, Berlin
  • Sánchez-Flores, S., The Lie module structure on the Hochschild cohomology groups of monomial algebras with radical square zero (2008) J. Algebra, 320 (12), pp. 4249-4269
  • Sánchez-Flores, S., (2009) La Structure De Lie De La Cohomologie De Hochschild D’algèbres Monomiales, Montpellier II, , https://tel.archives-ouvertes.fr/tel-00464064/document
  • Sköldberg, E., Contracting homotopy for Bardzell’s resolution (2008) Math. Proc. R. Ir. Acad., 108 (2), pp. 111-117
  • Strametz, C., The Lie algebra structure on the first Hochschild cohomology group of a monomial algebra (2006) J. Algebra Appl., 5 (3), pp. 245-270

Citas:

---------- APA ----------
Artenstein, D., Lanzilotta, M. & Solotar, A. (2019) . Gerstenhaber Structure on Hochschild Cohomology of Toupie Algebras. Algebras and Representation Theory.
http://dx.doi.org/10.1007/s10468-019-09854-y
---------- CHICAGO ----------
Artenstein, D., Lanzilotta, M., Solotar, A. "Gerstenhaber Structure on Hochschild Cohomology of Toupie Algebras" . Algebras and Representation Theory (2019).
http://dx.doi.org/10.1007/s10468-019-09854-y
---------- MLA ----------
Artenstein, D., Lanzilotta, M., Solotar, A. "Gerstenhaber Structure on Hochschild Cohomology of Toupie Algebras" . Algebras and Representation Theory, 2019.
http://dx.doi.org/10.1007/s10468-019-09854-y
---------- VANCOUVER ----------
Artenstein, D., Lanzilotta, M., Solotar, A. Gerstenhaber Structure on Hochschild Cohomology of Toupie Algebras. Algebr Represent Theory. 2019.
http://dx.doi.org/10.1007/s10468-019-09854-y