New Braided Crossed Categories and Drinfel'd Quantum Double for Weak Hopf Group Coalgebras |
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Authors: | A Van Daele |
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Institution: | Department of Mathematics , K.U. Leuven , Heverlee, Belgium |
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Abstract: | A simple and nice structure theorem for orthogroups was given by Petrich in 1987. In this paper, we consider a generalized orthogroup, that is, a quasi-completely regular semigroup with a band of idempotents in which its set of regular elements, namely, RegS, forms an ideal of S. A method of construction of such semigroups is provided and as a result, the Petrich structure theorem of orthogroups becomes an immediate corollary of our theorem on generalized orthogroups. An example of such generalized orthogroup is also constructed. This example provides some useful information for the construction of various kinds of quasi-completely regular semigroups. |
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Keywords: | Braided crossed category Drinfel'd quantum double Turaev category Unifying Hopf group-coalgebra Weak Hopf algebra Weak Hopf group-coalgebra Weak Hopf group-comodule Yetter–Drinfel'd module |
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