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)

Abstract

The Hopf algebra generated by the l-functionals on the quantum double C_q[G] ⋈ C_q[G] is considered, where C_q[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 C_q[G]^op ⋈ U_q(g). This proves a conjecture by T. Hodges. As an algebra it can be embedded into U_q(g) ⊗ U_q(g). Here it is proven that there is no bialgebra structure on U_q(g) ⊗ U_q(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 C_q[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
• Status: Published
• Refereed: Yes
• 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: 0021-8693
• ISSN (Online): 1793-6500