FRT-duals as quantum enveloping algebras

Kraehmer, U. (2003) FRT-duals as quantum enveloping algebras. Journal of Algebra, 264(1), pp. 68-81. (doi: 10.1016/S0021-8693(03)00116-9)

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The Hopf algebra generated by the l-functionals on the quantum double Cq[G] ⋈ Cq[G] is considered, where Cq[G] is the coordinate algebra of a standard quantum group and q is not a root of unity. It is shown to be isomorphic to Cq[G]op ⋈ Uq(g). This proves a conjecture by T. Hodges. As an algebra it can be embedded into Uq(g) ⊗ Uq(g). Here it is proven that there is no bialgebra structure on Uq(g) ⊗ Uq(g), for which this embedding becomes a homomorphism of bialgebras. In particular, it is not an isomorphism. As a preliminary a lemma of Hodges concerning the structure of l-functionals on Cq[G] is generalized. For the classical groups a certain choice of root vectors is expressed in terms of l-functionals. A formula for their coproduct is derived.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Kraehmer, Dr Ulrich
Authors: Kraehmer, U.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Algebra
ISSN (Online):1793-6500

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