English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Potential algebras with few generators

MPS-Authors
/persons/resource/persons235490

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

/persons/resource/persons253155

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

External Ressource
Fulltext (public)

arXiv:1806.06829.pdf
(Preprint), 583KB

Supplementary Material (public)
There is no public supplementary material available
Citation

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


Cite as: http://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.