Quotients of the Highwater algebra and its cover
Franchi, Clara Mainardis, Mario McInroy, Justin
Franchi, Clara
Mainardis, Mario
McInroy, Justin
Advisors
Editors
Other Contributors
EPub Date
Publication Date
2023-11-15
Submitted Date
Collections
Files
Other Titles
Abstract
Primitive axial algebras of Monster type are a class of non-associative algebras with a strong link to finite (especially simple) groups. The motivating example is the Griess algebra, with the Monster as its automorphism group. A crucial step towards the understanding of such algebras is the explicit description of the 2-generated symmetric objects. Recent work of Yabe, and Franchi and Mainardis shows that any such algebra is either explicitly known, or is a quotient of the infinite-dimensional Highwater algebra H, or its characteristic 5 cover Ĥ. In this paper, we complete the classification of symmetric axial algebras of Monster type by determining the quotients of H and Ĥ. We proceed in a unified way, by defining a cover of H in all characteristics. This cover has a previously unseen fusion law and provides an insight into why the Highwater algebra has a cover which is of Monster type only in characteristic 5.
Citation
Franchi, C., Mainardis, M., & McInroy, J. (2023). Quotients of the Highwater algebra and its cover. Journal of Algebra, 640, 432-476. https://doi.org/10.1016/j.jalgebra.2023.11.009
Publisher
Elsevier
Journal
Journal of Algebra
Research Unit
DOI
10.1016/j.jalgebra.2023.11.009
PubMed ID
PubMed Central ID
Type
Article
Language
Description
© 2023 The Author(s). Published by Elsevier Inc.
Series/Report no.
ISSN
0021-8693
EISSN
1090-266X