On the simple representations of generalized quantum groups and quantum doubles

DOI10.1016/j.jalgebra.2007.11.037zbMath1236.17026OpenAlexW2069491101MaRDI QIDQ933369

David E. Radford, Hans-Juergen Schneider

Publication date: 21 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2007.11.037

zbMATH Keywords

quantum groupHopf algebrahighest weightsimple representation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (17)

On the Grothendieck rings of generalized Drinfeld doubles ⋮ Indecomposable decomposition of tensor products of modules over Drinfeld doubles of Taft algebras ⋮ Simple modules of the quantum double of the Nichols algebra of unidentified diagonal type 𝔲𝔣𝔬(7) ⋮ On projective modules over finite quantum groups ⋮ The Second Indicator and the Trace of the Antipode for Representations of a Class of Hopf Algebras of Andruskiewitch-Schneider Type ⋮ Complete reducibility theorems for modules over pointed Hopf algebras. ⋮ Yetter-Drinfeld modules under cocycle twists. ⋮ On Nichols algebras over basic Hopf algebras ⋮ Calabi-Yau pointed Hopf algebras of finite Cartan type. ⋮ EXAMPLES OF POINTED COLOR HOPF ALGEBRAS ⋮ Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type ⋮ The R-matrix of quantum doubles of Nichols algebras of diagonal type ⋮ Representations of pointed Hopf algebras and their Drinfel'd quantum doubles. ⋮ Finite-dimensional Nichols algebras over dual Radford algebras ⋮ On Hopf algebras with triangular decomposition ⋮ Pointed Hopf algebras -- from enveloping algebras to quantum groups and beyond. ⋮ Classification of finite-dimensional irreducible representations of generalized quantum groups via Weyl groupoids

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• Introduction to quantum groups

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