当前位置: X-MOL 学术Forum Math. Sigma › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A class of continuous non-associative algebras arising from algebraic groups including
Forum of Mathematics, Sigma ( IF 1.389 ) Pub Date : 2021-01-14 , DOI: 10.1017/fms.2020.66
Maurice Chayet , Skip Garibaldi

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.

中文翻译:

由代数群产生的一类连续非结合代数,包括

我们给出一个结构,它采用一个简单的线性代数群G在一个域上并产生一个可交换的、统一的和简单的非结合代数一种在那个领域。这种结构的两个吸引力是(1)当G有类型 $E_8$ , 代数一种通过将一个单元与 3875 维表示相邻而获得;(2) 它是有效的,因为产品运行在一种可以在计算机上实现。代数的描述 $E_8$ 案子已经被请求了一段时间,最近的证据增加了人们的兴趣 $E_8$ 是该代数的完全自同构群。我们构造得到的代数有一个不寻常的皮尔斯谱。
更新日期:2021-01-14
down
wechat
bug