Title
PBW deformations of Koszul algebras over a nonsemisimple ring PBW deformations of Koszul algebras over a nonsemisimple ring
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Berlin ,
Subject
Mathematics
Source (journal)
Mathematische Zeitschrift. - Berlin
Volume/pages
279(2015) :1-2 , p. 185-210
ISSN
0025-5874
ISI
000347831200008
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Let be a generalized Koszul algebra over a finite dimensional algebra . We construct a bimodule Koszul resolution of when the projective dimension of equals two. Using this we prove a Poincar,-Birkhoff-Witt (PBW) type theorem for a deformation of a generalized Koszul algebra. When the projective dimension of 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).
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