Irreducible representations of a class of quantum doubles

DOI10.1006/jabr.1999.8135zbMath0952.16032OpenAlexW1971097240MaRDI QIDQ1972042

Hui-Xiang Chen

Publication date: 13 August 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1999.8135

zbMATH Keywords

tensor productsquantum Yang-Baxter equationirreducible representationsirreducible modulesquantum doublespointed Hopf algebrascompletely reducible modules

Mathematics Subject Classification ID

Related Items (26)

Indecomposable decomposition of tensor products of modules over Drinfeld doubles of Taft algebras ⋮ IRREDUCIBLE REPRESENTATIONS OF A CLASS OF FINITE-DIMENSIONAL ALGEBRAS ⋮ Tensor representations for the Drinfeld double of the Taft algebra ⋮ FINITE-DIMENSIONAL REPRESENTATIONS OF QUANTUM GROUP ⋮ McKay matrices for finite-dimensional Hopf algebras ⋮ A quantum subgroup depth ⋮ An asymptotic cell category for cyclic groups ⋮ On projective modules over finite quantum groups ⋮ Hopf \(*\)-algebra structures on \(H(1,q)\). ⋮ Simple modules of small quantum groups at dihedral groups ⋮ Grothendieck Groups of a Class of Quantum Doubles ⋮ On oriented quantum algebras derived from representations of the quantum double of a finite-dimensional Hopf algebra. ⋮ Green rings of Drinfeld doubles of Taft algebras ⋮ The Green ring of Drinfeld double \(D(H_4)\). ⋮ REPRESENTATIONS OF A CLASS OF DRINFELD'S DOUBLES ⋮ Representations of Finite Dimensional Pointed Hopf Algebras Over ℤ_n ⋮ Quantum double of \(\text U_q((\mathfrak{sl}_2)^{\leqslant 0})\) ⋮ Some Hopf algebras related to sl2 ⋮ Factorization of simple modules for certain pointed Hopf algebras. ⋮ Tensor Products of Modules Over a Certain Class of Quantum Doubles ⋮ Four-dimensional Yetter-Drinfeld module algebras over \(H_4\). ⋮ A Trace-Like Invariant for Representations of Hopf Algebras ⋮ On Hopf algebras with triangular decomposition ⋮ Finite-dimensional representations of a quantum double ⋮ Representation theory of the Drinfeld doubles of a family of Hopf algebras. ⋮ Representations of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one.

Cites Work

• Yetter-Drinfel'd categories associated to an arbitrary bialgebra
• A necessary and sufficient condition for a finite-dimensional Drinfel'd double to be a ribbon Hopf algebra
• Biinvertible actions of Hopf algebras
• Algebraic aspects of the quantum Yang-Baxter equation
• Minimal quasitriangular Hopf algebras
• QUASITRIANGULAR HOPF ALGEBRAS AND YANG-BAXTER EQUATIONS
• Quantum groups and representations of monoidal categories
• A class of noncommutative and noncocommutative hopf algebras: the quantum version
• Cleft extensions for a hopf algebra generated by a nearly primitive element
• Invariants of Links and 3-Manifolds Obtained from Hopf Algebras
• The Order of the Antipode of Finite-dimensional Hopf Algebra
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