Weak Hopf algebras corresponding to Cartan matrices

Details Weak Hopf algebras corresponding to Cartan matrices Weak Hopf algebras corresponding to Cartan matrices

2005-04-24

arxiv.org/abs/math/0504494v1

Journal of Mathematical Physics 46, 073502 (2005)

Mathematics

Quantum Algebra

21 pages

Scientific paper

10.1063/1.1933063

We replace the group of group-like elements of the quantized enveloping algebra $U_q({\frak{g}})$ of a finite dimensional semisimple Lie algebra ${\frak g}$ by some regular monoid and get the weak Hopf algebra ${\frak{w}}_q^{\sf d}({\frak g})$. It is a new subclass of weak Hopf algebras but not Hopf algebras. Then we devote to constructing a basis of ${\frak{w}}_q^{\sf d}({\frak g})$ and determine the group of weak Hopf algebra automorphisms of ${\frak{w}}_q^{\sf d}({\frak g})$ when $q$ is not a root of unity.

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