Geodesic
A class of continuous non-associative algebras arising from algebraic groups including $E_8$
Forum of Mathematics, Sigma, Tome 9 (2021)

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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. 
@article{10_1017_fms_2020_66,
     author = {Maurice Chayet and Skip Garibaldi},
     title = {A class of continuous non-associative algebras arising from algebraic groups including $E_8$},
     journal = {Forum of Mathematics, Sigma},
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     year = {2021},
     doi = {10.1017/fms.2020.66},
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Maurice Chayet; Skip Garibaldi. A class of continuous non-associative algebras arising from algebraic groups including $E_8$. Forum of Mathematics, Sigma, Tome 9 (2021). doi: 10.1017/fms.2020.66

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