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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 | Document URI: | http://hdl.handle.net/1942/18124 | Link to publication/dataset: | http://link.springer.com/article/10.1007%2Fs00209-014-1362-y | 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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