PBW deformations of quadratic monomial algebras

A result of Braverman and Gaitsgory from 1996 gives necessary and sufficient conditions for a filtered algebra to be a Poincaré-Birkhoff-Witt (PBW) deformation of a Koszul algebra. The main theorem in this paper establishes conditions equivalent to the Braverman-Gaitsgory Theorem to efficiently dete...

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Bibliographic Details
Published inCommunications in algebra Vol. 47; no. 7; pp. 2670 - 2688
Main Authors Cline, Zachary, Estornell, Andrew, Walton, Chelsea, Wynne, Matthew
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.07.2019
Taylor & Francis Ltd
Subjects
Algebra
Deformation
directed graph
monomial algebra
Poincaré-Birkhoff-Witt deformation
quadratic algebra
Theorems
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ISSN0092-7872
1532-4125
DOI10.1080/00927872.2018.1536757

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Summary:A result of Braverman and Gaitsgory from 1996 gives necessary and sufficient conditions for a filtered algebra to be a Poincaré-Birkhoff-Witt (PBW) deformation of a Koszul algebra. The main theorem in this paper establishes conditions equivalent to the Braverman-Gaitsgory Theorem to efficiently determine PBW deformations of quadratic monomial algebras. In particular, a graphical interpretation is presented for this result, and we discuss circumstances under which some of the conditions of this theorem need not be checked. Several examples are also provided. Finally, with these tools, we show that each quadratic monomial algebra admits a nontrivial PBW deformation.
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ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2018.1536757