New Quantum Groups by Double-Bosonisation

Abstract

We obtain new family of quasitriangular Hopf algebras $C^{0|n}_q\lcross \widetilde{U_q(su_n)}\rcross C^{0|n}_q$ via the author's recent double-bosonisation construction for new quantum groups. They are versions of $U_q(s{u}_{n+1})$ with a fermionic rather than bosonic quantum plane of roots adjoined to $U_q(s{u}_n)$. We give the $n=2$ case in detail. We also consider the anyonic-double of an anyonic ($Z/nZ$-graded) braided group and the double-bosonisation of the free braided group in $n$ variables.

9 pp Latex. Forgot to mention U(1) in Intro (no change in rest paper)

References in corpus (2)

• Free Braided Differential Calculus, Braided Binomial Theorem and the Braided Exponential Map
• Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group

Cited by in corpus (4)

• Double-bosonization and Majid's conjecture, (I): rank-induction of $ABCD$
• Double-bosonization and Majid's Conjecture, (IV): Type-Crossings from $A$ to $BCD$
• Braided enveloping algebras associated to quantum parabolic subalgebras
• Double crossed biproducts and related structures