## 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 language | English (US) |
---|---|

Pages (from-to) | 2670-2688 |

Number of pages | 19 |

Journal | Communications in Algebra |

Volume | 47 |

Issue number | 7 |

DOIs | |

State | Published - Jul 3 2019 |

## Keywords

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

## ASJC Scopus subject areas

- Algebra and Number Theory