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Title: PBW deformations of Koszul algebras over a nonsemisimple ring
Authors: He, Jiwei
Van Oystaeyen, Fred
ZHANG, Yinhuo 
Issue Date: 2015
Source: MATHEMATISCHE ZEITSCHRIFT, 279 (1), p. 185-210
Abstract: Let B be a generalized Koszul algebra over a finite dimensional algebra S. We construct a bimodule Koszul resolution of B when the projective dimension of SB equals two. Using this we prove a Poincaré–Birkhoff–Witt (PBW) type theorem for a deformation of a generalized Koszul algebra. When the projective dimension of SB is greater than two, we construct bimodule Koszul resolutions for generalized smash product algebras obtained from braidings between finite dimensional algebras and Koszul algebras, and then prove the PBW type theorem. The results obtained can be applied to standard Koszul Artin–Schelter Gorenstein algebras in the sense of Minamoto and Mori (Adv Math 226:4061–4095, 2011).
Notes: [He, Ji-Wei] Shaoxing Coll Arts & Sci, Dept Math, Shaoxing 312000, Zhejiang, Peoples R China. [Van Oystaeyen, Fred] Univ Antwerp, Dept Math & Comp Sci, B-2020 Antwerp, Belgium. [Zhang, Yinhuo] Univ Hasselt, Dept WNI, B-3590 Diepenbeek, Belgium.
Keywords: generalized Koszul algebra; PBW deformation; bimodule Koszul resolution; Artin–Schelter Gorenstein algebra
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ISSN: 0025-5874
e-ISSN: 1432-1823
DOI: 10.1007/s00209-014-1362-y
ISI #: 000347831200008
Rights: © Springer-Verlag Berlin Heidelberg 2014.
Category: A1
Type: Journal Contribution
Validations: ecoom 2016
Appears in Collections:Research publications

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