Potential algebras with few generators

Iyudu, Natalia; Shkarin, Stanislav

doi:10.1017/S0017089520000233

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Potential algebras with few generators

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Iyudu, Natalia
Max Planck Institute for Mathematics, Max Planck Society;

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Shkarin, Stanislav
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1017/S0017089520000233
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arXiv:1806.06829.pdf
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Citation

Iyudu, N., & Shkarin, S. (2020). Potential algebras with few generators. Glasgow Mathematical Journal, 62(S1), S28-S76. doi:10.1017/S0017089520000233.

Cite as: https://hdl.handle.net/21.11116/0000-0007-81C3-A

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.