Axial Algebras: Questions and Conjectures
Year: 2026
Type: article
Abstract: Axial algebras are non-associative algebras generated by idempotents, called axes, whose adjoint action satisfies a fusion law. When this fusion law is graded, axes naturally lead to automorphisms of the algebra, and so such axial algebras are inextricably linked with groups. This article is meant to complement the recent survey \cite{ms} by significantly expanding the list of interesting open problems suggested by the specialists in the field, and providing a further discussion of the related concepts and available results.
Source: Communications in Mathematics
DOI: 10.46298/cm.19581
Authors: Ilya Gorshkov, Sergey Shpectorov
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Russian Science Foundation
OpenAlex ID: W7166671403