PBW deformations of quadratic monomial algebras

Zachary Cline, Andrew Estornell, Chelsea Walton, Matthew Wynne

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2670-2688
Number of pages19
JournalCommunications in Algebra
Volume47
Issue number7
DOIs
StatePublished - Jul 3 2019

Keywords

  • Poincaré-Birkhoff-Witt deformation
  • directed graph
  • monomial algebra
  • quadratic algebra

ASJC Scopus subject areas

  • Algebra and Number Theory

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