Classification of derivation-simple color algebras related to locally finite derivations

Abstract

We classify the pairs $(A,D)$ consisting of an $(\epsilon ,\Gamma )$-olor-commutative associative algebra $A$ with an identity element over an algebraically closed field $F$ of characteristic zero and a finite dimensional subspace $D$ of $(\epsilon ,\Gamma )$-color-commutative locally finite color-derivations of $A$ such that $A$ is $\Gamma$-graded $D$-simple and the eigenspaces for elements of $D$ are $\Gamma$-graded. Such pairs are the important ingredients in constructing some simple Lie color algebras which are in general not finitely-graded. As some applications, using such pairs, we construct new explicit simple Lie color algebras of generalized Witt type, Weyl type.

15 pages

References in corpus (1)

• Cohomology of Lie superalgebras and of their generalizations

Cited by in corpus (3)

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• Classification of minimal ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie (super)algebras and some applications