论文标题
由代数组引起的一类连续非缔合代数，包括$ e_8 $
A class of continuous non-associative algebras arising from algebraic groups including $E_8$
论文作者
论文摘要
我们提供了一个在一个字段上采用简单的线性代数组$ g $的结构，并在该领域产生了交换，Unital和简单的非缔合代数$ a $。该结构的两个景点是（1）当$ g $具有类型$ e_8 $时，代数$ a $是通过将单元毗邻3875维表示而获得的，并且（2）是有效的，因为$ a $ a $可以在计算机上实施。一段时间以来，已要求对$ e_8 $案件中的代数的描述，并且最近证明了$ e_8 $是该代数的完整自动形态组。通过我们的构造获得的代数具有不寻常的PEIRCE频谱。
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.
