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Quotients of the Highwater algebra and its cover.
- Source :
-
Journal of Algebra . Feb2024, Vol. 640, p432-476. 45p. - Publication Year :
- 2024
-
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 H ˆ. In this paper, we complete the classification of symmetric axial algebras of Monster type by determining the quotients of H and H ˆ. 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*AUTOMORPHISM groups
*FINITE simple groups
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 640
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 174035760
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2023.11.009