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- W2066826579 abstract "In this paper, we investigate weak Hopf algebras introduced in Li (J Algebra 208:72–100, 1998; Commun Math Phys 225:191–217, 2002) corresponding to quantum algebras U q (f (K, H)) (see Wang et al. in Commun Algebra 30:2191–2211, 2002). A new class of algebras is defined, which is denoted by $${mathfrak{w}U^{d}_q.}$$ For d = ((1, 1) | (1, 1)), denote $${mathfrak{w}U^{d}_q}$$ briefly by $${mathfrak{w}_{1}U_q}$$ ; for d = ((0, 0) | (0, 0)), denote $${mathfrak{w}U^{d}_q}$$ briefly by $${mathfrak{w}_{2}U_q.}$$ In some cases, the necessary and sufficient conditions for $${mathfrak{w}_{1}U_q}$$ and $${mathfrak{w}_{2}U_q}$$ to be weak Hopf algebras are given. The PBW bases of $${mathfrak{w}_{1}U_q}$$ and $${mathfrak{w}_{2}U_q}$$ are presented. Finally, representations and the center of $${mathfrak{w}_{1}U_q}$$ are characterized over $${mathbb{C}}$$ with $${q in mathbb{C}}$$ which is not a root of unity." @default.
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- W2066826579 date "2012-04-05" @default.
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- W2066826579 title "Weak Hopf algebras corresponding to quantum algebras U q (f (K, H))" @default.
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- W2066826579 doi "https://doi.org/10.1007/s40065-012-0014-5" @default.
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