Weak Hopf algebras corresponding to $U_q[sl_n]$

Details Weak Hopf algebras corresponding to $U_q[sl_n]$ Weak Hopf algebras corresponding to $U_q[sl_n]$

2003-07-31

arxiv.org/abs/math/0307391v1

J. Math. Phys. 44 (2003) 5250-5267

Mathematics

Quantum Algebra

23 pages

Scientific paper

10.1063/1.1616999

We investigate the weak Hopf algebras of Li based on $U_q[sl_n]$ and Sweedler's finite dimensional example. We give weak Hopf algebra isomorphisms between the weak generalisations of $U_q[sl_n]$ which are ``upgraded'' automorphisms of $U_q[sl_n]$ and hence give a classification of these structures as weak Hopf algebras. We also show how to decompose these examples into a direct sum which leads to unexpected isomorphisms between their algebraic structure.

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