The Lie algebra of the structure group of a power-associative algebra.

Abstract:

For a strictly power-associative algebra $A$ with identity let $S$ be the span of the transitivity set of the identity under the action of the structure group. The main result of the paper is that the Lie algebra of the structure group is a subalgebra of the direct sum of the derivation algebra of ${A^ + }$ and the space of left multiplications in ${A^ + }$ by elements of $S$, and is equal to this sum if the characteristic is 0. It is also shown that $S$ is a Jordan subalgebra of ${A^ + }$.