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arXiv · 0910.0550

Actor of an alternative algebra

José Manuel Casas·Tamar Datuashvili·Manuel Ladra
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Abstract

We define a category $\galt$ of g-alternative algebras over a field $F$ and present the category of alternative algebras $\alt$ as a full subcategory of $\galt$; in the case $\ch F\neq 2$, we have $\alt=\galt$. For any g-alternative algebra $A$ we give a construction of a universal strict general actor $\cB(A)$ of $A$. We define the subset $\asoci(A)$ of $A$, and show that it is a $\cB(A)$-substructure of $A$. We prove that if $\asoci(A)=0$, then there exists an actor of $A$ in $\galt$ and $\act(A)=\cB(A)$. In particular, we obtain that if $A$ is anticommutative and $\ann(A)=0$, then there exists an actor of $A$ in $\galt$; from this, under the same conditions, we deduce the existence of an actor in $\alt$.

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José Manuel Casas, Tamar Datuashvili, Manuel Ladra. 2009-10-03. Actor of an alternative algebra. https://arxiv.org/abs/0910.0550

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