Color Lie superalgebras and Hopf algebras
The author is concerned with extending the theorem asserting the equivalence of the category of primitively generated Hopf algebras to the category of (restricted) Lie algebras [cf. \textit{J. W. Milnor} and \textit{J. C. Moore}, Ann. Math., II. Ser. 81, 211-264 (1965; Zbl 0163.28202)] to the case of colour Lie superalgebras. Here the primitively generated Hopf algebra becomes a Hopf algebra \(H\) whose semigroup (i.e. grouplike) elements form an abelian group \(G=G(H)\), while \(H\) is generated by its relatively primitive elements (i.e. satisfying \(\Delta(\delta)=\delta\otimes 1+s\otimes\delta\), for some \(s\in G(H)\)), which `supercommute' with the elements of \(G\). The notions of colour Lie superalgebra and \(\varepsilon\)-bialgebra are carefully explained and the proof proceeds by an induction on the natural filtration.
category of primitively generated Hopf algebras
scientific article; zbMATH DE number 907279
scientific article