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Free keywords:
Mathematics, Rings and Algebras, Mathematical Physics, Algebraic Topology, Group Theory, Quantum Algebra
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.
