Algebras based on Yang-Baxter operators (Q1322740)

For an abelian group \(\Gamma\), \(\Gamma\)-graded algebras and \(\varepsilon\) Lie algebras (with \(\varepsilon\) a commutation factor on \(\Gamma\)) were introduced by \textit{M. Scheunert} [J. Math. Phys. 20, 712-720 (1979; Zbl 0423.17003)] as an extension of associative superalgebras and Lie superalgebras. In the present paper, Yang-Baxter operators on a \(\Gamma\)- graded vector space are defined, and used to construct the \(\Gamma\)- graded versions of \(S\)-exterior algebras, \(S\)-symmetric algebras, bialgebras and Hopf algebras.