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Color Lie superalgebras and Hopf algebras. (English. Russian original) Zbl 0856.16039

Algebra Logic 34, No. 4, 232-241 (1995); translation from Algebra Logika 34, No. 4, 420-436 (1995).
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. J. W. Milnor and 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.
Reviewer: P.M.Cohn (London)

MSC:

16W30 Hopf algebras (associative rings and algebras) (MSC2000)
17B70 Graded Lie (super)algebras
16D90 Module categories in associative algebras

Citations:

Zbl 0163.28202
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References:

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