LAUSR

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$\frak L$ admitting a quasi-multiplicative basis, with restrictions neither on the dimensions nor on the base field F$\mathbb F$ and study its structure. We state that if L$\frak L$ admits a quasi-multiplicative basis then it decomposes as L=U⊕(∑Jk)$\mathfrak {L} ={\mathcal U} \oplus (\sum \limits {\frak J}_{k})$ with any Jk${\frak J}_{k}$ a well described color gLt-ideal of L$\frak L$ admitting also a quasi-multiplicative basis, and U${\mathcal U}$ a linear subspace of V$\mathbb V$. Also the minimality of L$\frak L$ 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$\frak L$.