On antiflexible algebras

Abstract:

In this paper we begin a classification of simple and semisimple totally antiflexible algebras (finite-dimensional) over splitting fields of char. $\ne 2,3$. For such an algebra $A$, let $P$ be the largest associative ideal in ${A^ + }$ and let ${N^ + }$ be the radical of $P$. We determine all simple and semisimple totally antiflexible algebras in which $N \cdot N = 0$. Defining $A$ to be of type $(m,n)$ if ${N^ + }$ is nilpotent of class $m$ with $\dim A = n$, we then characterize all simple nodal totally anti-flexible algebras (over fields of char. $\ne 2,3$) of types $(n,n)$ and $(n - 1,n)$ and give preliminary results for certain other types.