A Generalized Drinfeld Quantum Double Construction Based on Weak Hopf Algebras |
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| Authors: | Haixing Zhu |
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| Institution: | Department of Mathematics , Southeast University , Nanjing, Jiangsu, China |
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| Abstract: | Let B and H be weak Hopf algebras with bijective antipodes S B and S H , respectively. Based on a compatible weak Hopf dual pairing (B, H, σ), we construct a generalized Drinfeld quantum double 𝔻(B, H) which is a weak T-coalgebra over a twisted semi-direct square of groups. In particular, when B and H are finite dimensional and the above pairing map σ is nondegenerate, 𝔻(B, H) admits a nontrivial quasitriangular structure. Some explicit examples are given as an application of our theory. |
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| Keywords: | Quasitriangular structures Weak Hopf algebras Weak Hopf dual pairings Weak T-coalgebras |
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