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Abstract:

In this article we establish an explicit link between the classical theory of deformations à la Gerstenhaber (and a fortiori with the Hochschild cohomology) and (weak) PBW-deformations of homogeneous algebras. Our point of view is of cohomological nature. As a consequence, we recover a theorem by R. Berger and V. Ginzburg, which gives a precise condition for a filtered algebra to satisfy the so-calledPBWproperty, under certain assumptions. © European Mathematical Society.

Registro:

Documento: Artículo
Título:PBW-deformations and deformations à la Gerstenhaber of N-Koszul algebras
Autor:Herscovich, E.; Solotar, A.; Suárez-Álvarez, M.
Filiación:Fakultät Für Mathematik, Universität Bielefeld, 33615 Bielefeld, Germany
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, 1428, Buenos Aires, Argentina
Palabras clave:Deformation theory; Hochschild cohomology; Koszul algebras
Año:2014
Volumen:8
Número:2
Página de inicio:505
Página de fin:539
DOI: http://dx.doi.org/10.4171/JNCG/163
Título revista:Journal of Noncommutative Geometry
Título revista abreviado:J. Noncommunitative Geom.
ISSN:16616952
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16616952_v8_n2_p505_Herscovich

Referencias:

  • Berger, R., Ginzburg, V., Higher symplectic reflection algebras and non-homogeneous N-Koszul property (2006) J. Algebra, 304, pp. 577-601. , Zbl 151.16026 MR 2256407
  • Berger, R., Marconnet, N., Koszul and Gorenstein properties for homogeneous algebras (2006) Algebr. Represent. Theory, 9, pp. 67-97. , Zbl 1125.16017 MR 2233117
  • Braverman, A., Gaitsgory, D., Poincaré-birkhoff-witt theorem for quadratic algebras of koszul type (1996) J. Algebra, 181, pp. 315-328. , Zbl 0860.17002 MR 1383469
  • Chriss, N., Ginzburg, V., (1997) Representation Theory and Complex Geometry, , Birkhäuser, Boston. Zbl 0879.22001 MR 1433132
  • Fløystad, G., Vatne, J.E., PBW-deformations of N-Koszul algebras (2006) J. Algebra, 302, pp. 116-155. , Zbl 1159.16026 MR 2236596
  • Gerstenhaber, M., On the deformation of rings and algebras (1964) Ann. of Math., 79 (2), pp. 59-103. , Zbl 0123.03101 MR 0171807
  • Gordon, I.G., Symplectic reflection algebras Trends in representation theory of algebras and related topics (2008) EMS Ser. Congr. Rep., Eur. Math. Soc., , Zürich, 285-347. Zbl 1200.16045 MR 2484729
  • Guccione, J.A., Guccione, J.J., Redondo, M.J., Solotar, A., Villamayor, O.E., Cyclic homology of algebras with one generator (1991) K-Theory, 5, pp. 51-69. , Zbl 0743.13008 MR 1141335

Citas:

---------- APA ----------
Herscovich, E., Solotar, A. & Suárez-Álvarez, M. (2014) . PBW-deformations and deformations à la Gerstenhaber of N-Koszul algebras. Journal of Noncommutative Geometry, 8(2), 505-539.
http://dx.doi.org/10.4171/JNCG/163
---------- CHICAGO ----------
Herscovich, E., Solotar, A., Suárez-Álvarez, M. "PBW-deformations and deformations à la Gerstenhaber of N-Koszul algebras" . Journal of Noncommutative Geometry 8, no. 2 (2014) : 505-539.
http://dx.doi.org/10.4171/JNCG/163
---------- MLA ----------
Herscovich, E., Solotar, A., Suárez-Álvarez, M. "PBW-deformations and deformations à la Gerstenhaber of N-Koszul algebras" . Journal of Noncommutative Geometry, vol. 8, no. 2, 2014, pp. 505-539.
http://dx.doi.org/10.4171/JNCG/163
---------- VANCOUVER ----------
Herscovich, E., Solotar, A., Suárez-Álvarez, M. PBW-deformations and deformations à la Gerstenhaber of N-Koszul algebras. J. Noncommunitative Geom. 2014;8(2):505-539.
http://dx.doi.org/10.4171/JNCG/163