Weak Hopf algebras corresponding to $U_q[s{l}_n]$

Abstract

We investigate the weak Hopf algebras of Li based on $U_q[s{l}_n]$ and Sweedler's finite dimensional example. We give weak Hopf algebra isomorphisms between the weak generalisations of $U_q[s{l}_n]$ which are ``upgraded'' automorphisms of $U_q[s{l}_n]$ 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.

23 pages

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