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29 March 2024
 
  » arxiv » math.QA/0504494

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Weak Hopf algebras corresponding to Cartan matrices
Shilin Yang ;
Date 24 Apr 2005
Journal JOURNAL OF MATHEMATICAL PHYSICS 46, 073502 (2005) DOI: 10.1063/1.1933063
Subject Quantum Algebra; Rings and Algebras MSC-class: 17B37;16W30 | math.QA math-ph math.MP math.RA
AbstractWe 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.
Source arXiv, math.QA/0504494
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