Ma, Yao; Chen, Liangyun; Lin, Jie \(T^*\)-extensions of Lie color algebras. (Chinese. English summary) Zbl 1324.17026 Chin. Ann. Math., Ser. A 35, No. 5, 623-638 (2014). Summary: In this paper, the notion of \(T^*\)-extension of a Lie color algebra is introduced. Many properties of a Lie color algebra can be lifted to its \(T^*\)-extensions, such as nilpotency, solvability and decomposition. It is proved that every finite-dimensional nilpotent quadratic Lie color algebra \(A\) over an algebraically closed field of characteristic different from 2 is isometric to a \(T^*\)-extension of a nilpotent Lie color algebra \(B\), and the nilpotent length of \(B\) is at most half of that of \(A\). Moreover, the equivalence of \(T^*\)-extensions is investigated from the cohomological point of view. Cited in 1 Document MSC: 17B75 Color Lie (super)algebras 17B30 Solvable, nilpotent (super)algebras 17A45 Quadratic algebras (but not quadratic Jordan algebras) Keywords:\(T^*\)-extension; Lie color algebra; nilpotent; quadratic PDFBibTeX XMLCite \textit{Y. Ma} et al., Chin. Ann. Math., Ser. A 35, No. 5, 623--638 (2014; Zbl 1324.17026)