A class of continuous non-associative algebras arising from algebraic groups including $E_8$
| Autor: | Chayet, Maurice, Garibaldi, Skip |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Forum of Mathematics, Sigma, vol. 9 (2021), e6 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/fms.2020.66 |
| Popis: | We give a construction that takes a simple linear algebraic group $G$ over a field and produces a commutative, unital, and simple non-associative algebra $A$ over that field. Two attractions of this construction are that (1) when $G$ has type $E_8$, the algebra $A$ is obtained by adjoining a unit to the 3875-dimensional representation and (2) it is effective, in that the product operation on $A$ can be implemented on a computer. A description of the algebra in the $E_8$ case has been requested for some time, and interest has been increased by the recent proof that $E_8$ is the full automorphism group of that algebra. The algebras obtained by our construction have an unusual Peirce spectrum. Comment: v4 provides various expositional improvements. Results on E8 remain the same as in v1 |
| Databáze: | arXiv |
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