## 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.## References

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## Additional Information

**Tom De Medts**- Affiliation: Department of Mathematics: Algebra and Geometry, Ghent University, Krijgslaan 281–S25, 9000 Gent, Belgium
- MR Author ID: 701084
- ORCID: 0000-0002-9504-5353
- Email: tom.demedts@ugent.be
**Michiel Van Couwenberghe**- Affiliation: Department of Mathematics: Algebra and Geometry, Ghent University, Krijgslaan 281–S25, 9000 Gent, Belgium
- MR Author ID: 1361192
- ORCID: 0000-0001-8480-6586
- Email: michiel.vancouwenberghe@ugent.be
- Received by editor(s): May 5, 2020
- Received by editor(s) in revised form: March 30, 2021, and April 28, 2021
- Published electronically: September 16, 2021
- Additional Notes: Tom De Medts is the corresponding author

Michiel Van Couwenberghe is a Ph. D. fellow of the Research Foundation – Flanders (FWO) - © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**374**(2021), 8715-8774 - MSC (2020): Primary 20F29, 17A36, 17D99, 17B10, 20G05
- DOI: https://doi.org/10.1090/tran/8484
- MathSciNet review: 4337927