Non-associative Frobenius algebras for simply laced Chevalley groups

Tom De Medts; Michiel Van Couwenberghe

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arXiv · 2005.02625

Non-associative Frobenius algebras for simply laced Chevalley groups

Tom De Medts·Michiel Van Couwenberghe

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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 E8 acts by automorphisms. We also prove that these algebras admit the structure of (axial) decomposition algebras.

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BibTeX RIS

Tom De Medts, Michiel Van Couwenberghe. 2020-05-06. Non-associative Frobenius algebras for simply laced Chevalley groups. https://arxiv.org/abs/2005.02625

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