Abstract
In the first half of this paper, we define axial algebras: nonassociative commutative algebras generated by axes, that is, semisimple idempotents-the prototypical example of which is Griess' algebra [2] for the Monster group. When multiplication of eigenspaces of axes is controlled by fusion rules, the structure of the axial algebra is determined to a large degree. We give a construction of the universal Frobenius axial algebra on n generators with specified fusion rules, of which all n-generated Frobenius axial algebras with the same fusion rules are quotients. In the second half, we realise this construction in the Majorana/Ising/Vir(4, 3)-case on 2 generators, and deduce a result generalising Sakuma's theorem in VOAs [13].
Original language | English |
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Pages (from-to) | 394-424 |
Number of pages | 31 |
Journal | Journal of Algebra |
Volume | 421 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
Keywords
- Fusion rules
- Idempotents
- Monster group
- Nonassociative algebras