New Quantum Groups by Double-Bosonisation

Details New Quantum Groups by Double-Bosonisation New Quantum Groups by Double-Bosonisation

1996-10-02

arxiv.org/abs/q-alg/9610004v2

Czech.J.Phys.47:79-90,1997

Mathematics

Quantum Algebra

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

Scientific paper

10.1023/A:1021400329710

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 $U_q(su_{n+1})$ with a fermionic rather than bosonic quantum plane of roots adjoined to $U_q(su_n)$. 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.

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