Non-associative Frobenius algebras for simply laced Chevalley groups

De Medts, Tom; Van Couwenberghe, Michiel

doi:10.1090/tran/8484

Non-associative Frobenius algebras for simply laced Chevalley groups
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by Tom De Medts and Michiel Van Couwenberghe PDF

Trans. Amer. Math. Soc. 374 (2021), 8715-8774 Request permission

Abstract:

We provide an explicit construction for a class of commutative, non-associative algebras for each of the simple Chevalley groups of simply laced type. Moreover, we equip these algebras with an associating bilinear form, which turns them into Frobenius algebras. This class includes a 3876-dimensional algebra on which the Chevalley group of type $E_8$ acts by automorphisms. We also prove that these algebras admit the structure of (axial) decomposition algebras.

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