Weak Hopf algebras and some new solutions of the quantum Yang-Baxter equation

DOI10.1006/jabr.1998.7491zbMath0916.16020OpenAlexW2057649423MaRDI QIDQ1271899

Fang Li

Publication date: 12 July 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1998.7491

zbMATH Keywords

weak Hopf algebrasquantum Yang-Baxter equationfinite Clifford monoid algebrasquantum quasi-doublesquasi-braided almost bialgebras

Mathematics Subject Classification ID

Related Items (41)

The Right Braids, Quasi-braided Pre-tensor Categories, and General Yang–Baxter Operators ⋮ The extension of a quantized Borcherds superalgebra by a Hopf algebra ⋮ Structure of Quantum Doubles of Finite Clifford Monoids ⋮ Weak quantum Borcherds superalgebras and their representations ⋮ On quasi-bicrossed products of weak Hopf algebras. ⋮ On Hopf Algebras and Their Generalizations ⋮ Regular obstructed categories and topological quantum field theory ⋮ Weak Hopf algebras corresponding to Uq[sln] ⋮ Quantum doubles from a class of noncocommutative weak Hopf algebras ⋮ Extensions of quantum enveloping algebras ⋮ Weak Hopf algebras corresponding to quantum algebras \(U_q(f(K,H))\) ⋮ Double weak Hopf quiver and its path coalgebra ⋮ Weak rigid monoidal category ⋮ Quantum inverse semigroups ⋮ Constants of coordinate differential calculi defined by Yang-Baxter operators. ⋮ λ-TD algebras, generalized shuffle products and left counital Hopf algebras ⋮ Weak Hopf algebras with projection and weak smash bialgebra structures. ⋮ A compact quantum semigroup generated by an isometry ⋮ Unnamed Item ⋮ Hopf-Type Algebras ⋮ Weak Hopf algebras corresponding to Borcherds-Cartan matrices. ⋮ Lusztig symmetries and Poincare-Birkhoff-Witt basis for $\mathfrak {wU}_{r, s}^{\mathrm{d}}({\rm osp}(1|2n))$wUr,sd( osp (1|2n)) ⋮ Adjoint action for quantum algebra \(U_{r,t}\) ⋮ A class of weak Hopf algebras. ⋮ Infinite-dimensional compact quantum semigroup ⋮ Weak Hopf quivers, Clifford monoids and weak Hopf algebras. ⋮ Green rings of weak Hopf algebras based on generalized Taft algebras ⋮ Weak corings ⋮ Weak tensor category and related generalized Hopf algebras. ⋮ Singular Solutions to the Quantum Yang–Baxter Equations ⋮ The Structure of Weak Hopf Algebras Corresponding toU_q(sl₂) ⋮ A new solution to Hom-Yang–Baxter equations ⋮ Multiplication alteration by two-cocycles for bialgebras with weak antipode ⋮ Constructing Quasitriangular Hopf Algebras ⋮ Solutions of yang-baxter equation in an endomorphism semigroup and quasi-(co)braided almost bialgebras^∗ ⋮ S-Hopf Quivers and Semilattice Graded Weak Hopf Algebras ⋮ Braided version of Shirshov-Witt theorem ⋮ Weak Hopf algebras corresponding to Cartan matrices ⋮ Semilattice graded weak Hopf algebra and its related quantum G-double ⋮ Semisupermanifolds and regularization of categories, modules, algebras and Yang-Baxter equation ⋮ Automorphism group of green algebra of weak Hopf algebra corresponding to Sweedler Hopf algebra

Cites Work

• Biinvertible actions of Hopf algebras
• Left Hopf algebras
• Regularity of Semilattice Sums of Rings
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