Graded 2-generated axial algebras
Rings and Algebras
2020-05-08 v1 Group Theory
Abstract
Axial algebras are non-associative algebras generated by semisimple idempotents whose adjoint actions obey a fusion law. Axial algebras that are generated by two such idempotents play a crucial role in the theory. We classify all primitive 2-generated axial algebras whose fusion laws have two eigenvalues and all graded primitive 2-generated axial algebras whose fusion laws have three eigenvalues. This represents a significant broadening in our understanding of axial algebras.
Cite
@article{arxiv.2005.03577,
title = {Graded 2-generated axial algebras},
author = {Madeleine Whybrow},
journal= {arXiv preprint arXiv:2005.03577},
year = {2020}
}