doi: 10.1080/00927879708825884pmid: N/A
We characterize strongly purifiable subgroups of primary abelian groups to be intersections of finitely many pure hulls of these subgroups in given groups.
doi: 10.1080/00927879708825887pmid: N/A
We present a reduction of the adjoint representation of the Lie superalge-bra,sl(2,1) and a study of the quotient algebra B(c,k)= u/u(C−c)+u(D−kc), where c,k are two complex numbers. Under some additional conditions, we prove that every irreducible infinite dimensional representation of B(c,k) is faithful, and that B(C,K) is a primitive algebra. We give explicitly a set of generators of primitive degenerate ideal of infinite codimension. Essentially we prove that any minimal primitive ideal of u(sl(2,1)) is generated, as a 2-sided ideal, by its intersection with the algebra of gg-iuvariants.
doi: 10.1080/00927879708825888pmid: N/A
This paper is the sequel of a previous one [2] where we extended the Tannaka-Krein duality results to the non-commutative situation, i.e. to ‘quantum groupoids’. Here we extend those results to the quasi-monoidal situation, corresponding to ‘quasi-quantum groupoids’ as defined in [3] (‘quasi-’ stands for quasi-associativity a la Drinfeld). More precisely, let B be a commutative algebra over a field k. Given a tensor autonomous category τ,. we define the notion of a quasi-fibre functor ω:τ-proj B (here, ‘quasi-’ means without compatibility to associativity constraints). On the other hand, we define the notion of a transitive quasi-quantum groupoid over B. We then show that the category of tensor autonomous categories equipped with a quasi-fibre functor (with suitable morphisms), is equivalent to the category of transitive quasi-quantum groupoids (5.4.2) Moreover, we classify quasi-fibre functors for a semisimple tensor autonomous category (6.1.2), and give a few examples : a family of quantum groups having the same tensor category of representations as Sl2(C), but with non-isornorphic underlying coalgebras, constructed by means of an R-matrix introduced by Gurevich ([9]) in a manner suggested to the author by Lyubashenko (6.2.1 and 6.2.2), and quasi-quantum groups which cannot be obtained from quantum groups by a Drinfeld twist (6.2.1)
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