Cubical Species and Nonassociative Algebras

Nonassociative Algebras

On Nonassociative Division Algebras^)

A class of nonassociative algebras

A large class of nonassociative algebras, out of the Lie algebras has been studied, often with geometrical structures and sometimes on fondamental spaces as the spaces of Hochschild cohomology. In this paper, we propose to consider all these nonassociative algebras as algebras defined by the action of invariant subspaces of the symmetric group Σ 3 on the associator of the considered laws.

Structure and Representation of Nonassociative Algebras

xnA IN NONASSOCIATIVE ALGEBRAS, AND BASE-CHANGE

To any not-necessarily-associative finite-dimensional algebra A over a field k such that AA = A, i.e., such that every element may be written as a sum of products, we can associate the least integer n such that A can be written x1A+ · · ·+xnA for x1, . . . , xn ∈ A. If k is infinite, this invariant is unchanged under extension of base field. There are counterexamples if k is finite, or A infini...