2000 character limit reached
Potential algebras with few generators (1806.06829v1)
Published 18 Jun 2018 in math.RA, math-ph, math.AT, math.GR, math.MP, and math.QA
Abstract: We give a complete description of quadratic potential and twisted potential algebras on 3 generators as well as cubic potential and twisted potential algebras on 2 generators up to graded algebra isomorphisms under the assumption that the ground field is algebraically closed and has characteristic different from 2 or 3. We also prove that for two generated potential algebra necessary condition of finite-dimensionality is that potential contains terms of degree three, this answers a question of Agata Smoktunowicz and the first named author, formulated in [AN]. We clarify situation in case of arbitrary number of generators as well.