PBW deformations of quadratic monomial algebras |
| |
| Authors: | Zachary Cline Andrew Estornell Chelsea Walton Matthew Wynne |
| |
| Institution: | 1. Department of Mathematics, Temple University, Philadelphia, Pennsylvania, USA;2. Department of Computer Science &3. Engineering, Washington University, Saint Louis, Missouri, USA;4. Department of Mathematics, The University of Illinois at Urbana-Champaign, Urbana, Illinois, USA |
| |
| 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. |
| |
| Keywords: | Poincaré-Birkhoff-Witt deformation monomial algebra quadratic algebra directed graph |
|
|
