n-Ary Generalized Lie-Type Color Algebras Admitting a Quasi-multiplicative Basis

The class of generalized Lie-type color algebras contains the ones of generalized Lie-type algebras, of n -Lie algebras and superalgebras, commutative Leibniz n -ary algebras and superalgebras, among others. We focus on the class of generalized Lie-type color algebras L admitting a quasi-multiplicat...

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Bibliographic Details
Published in:Algebras and representation theory 2019-12, Vol.22 (6), p.1371-1386
Main Authors: Barreiro, Elisabete, Calderón, Antonio Jesús, Kaygorodov, Ivan, Sánchez, José María
Format: Article
Language:English
Subjects:
Algebra
Associative Rings and Algebras
Color
Commutative Rings and Algebras
Lie groups
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
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Summary:The class of generalized Lie-type color algebras contains the ones of generalized Lie-type algebras, of n -Lie algebras and superalgebras, commutative Leibniz n -ary algebras and superalgebras, among others. We focus on the class of generalized Lie-type color algebras L admitting a quasi-multiplicative basis, with restrictions neither on the dimensions nor on the base field F and study its structure. We state that if L admits a quasi-multiplicative basis then it decomposes as L = U ⊕ ( ∑ J k ) with any J k a well described color gLt-ideal of L admitting also a quasi-multiplicative basis, and U a linear subspace of V . Also the minimality of L is characterized in terms of the connections and it is shown that the above direct sum is by means of the family of its minimal color gLt-ideals, admitting each one a μ -quasi-multiplicative basis inherited by the one of L .
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-018-9824-2