منابع مشابه
Coloured quantum universal enveloping algebras
We define some new algebraic structures, termed coloured Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set H, corresponding to some parameter set Q, with the transformations of an algebra isomorphism group G, herein called colour group. Such transformations are labelled by some colour parameters, taking values in a colour set C. We show that vario...
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Various attempts to find a proper generalization of the notion of Lie algebra associated to a vector space V endowed with a non symmetric braiding c appeared in the literature. In this direction, we introduce and investigate a notion of braided Lie algebra (and the associated universal enveloping algebra) which turns out to be effective for the class of braided vector spaces (V, c) whose Nichol...
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Let A denote a bialgebra over a field k and let At = A[[t]] denote the ring of formal power series with coefficients in A. Assume that A is a free algebra over k with a basis of primitives. We give a simple construction which makes At a bialgebra deformation of A. Usually At is neither commutative nor cocommutative. This construction yields deformations of bialgebras associated with families of...
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Given an associative algebra A, and the category, C, of its finite dimensional modules, additional structures on the algebra A induce corresponding ones on the category C. Thus, the structure of a rigid quasi-tensor (braided monoidal) category on RepA is induced by an algebra homomorphism A → A ⊗ A (comultiplication), coassociative up to conjugation by Φ ∈ A (associativity constraint) and cocom...
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Quantized enveloping algebras have been widely studied, almost exclusively by theoretical means (see, for example, De Concini and Procesi, 1993; Jantzen, 1996; Lusztig, 1993). In this paper we consider the problem of computing with a quantized enveloping algebra. For this we need a basis of it, along with a method for computing the product of two basis elements. To this end we will use so-calle...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2011
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089511000310