Braided identities, quantum groups, and Clifford algebras
For the Lie algebra \({\mathfrak g}=sl^+_{n+1}\) (upper triangular matrices), the author constructs a deformation (quantum Lie algebra \({\mathfrak g}_q)\) and a generalized universal enveloping algebra \(U({\mathfrak g}_q)\) such that \(U({\mathfrak g}_q) =U_q({\mathfrak g})\), the quantum group of \({\mathfrak g}\), and such that \({\mathfrak g}_q\to {\mathfrak g}\) and \(U({\mathfrak g}_q) \to U({\mathfrak g})\) as \(q \to 1\). \({\mathfrak g}_q\) is a Lie algebra in a braided category and \(U({\mathfrak g}_q)\) is a braided Hopf algebra. Relations to Clifford algebras are discussed.
generalized universal enveloping algebra
scientific article; zbMATH DE number 1602929