Complete reducibility theorems for modules over pointed Hopf algebras.

DOI10.1016/j.jalgebra.2010.06.002zbMath1223.16010arXiv1001.3977OpenAlexW2963154936MaRDI QIDQ626696

Nicolás Andruskiewitsch, David E. Radford, Hans-Juergen Schneider

Publication date: 18 February 2011

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

Full work available at URL: https://arxiv.org/abs/1001.3977

zbMATH Keywords

quantum groupssimple modulespointed Hopf algebrascomplete reducibilityweight multiplicitiessimple finite-dimensional representations

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hopf algebras and their applications (16T05)

Related Items (28)

Pointed Hopf algebras with triangular decomposition. A characterization of multiparameter quantum groups ⋮ THE NICHOLS ALGEBRA OF SCREENINGS ⋮ Mini-workshop: Infinite dimensional Hopf algebras. Abstracts from the mini-workshop held April 13--19, 2014. ⋮ Multi-brace cotensor Hopf algebras and quantum groups ⋮ Simple modules of the quantum double of the Nichols algebra of unidentified diagonal type 𝔲𝔣𝔬(7) ⋮ Fusion in the entwined category of Yetter-Drinfeld modules of a rank-1 Nichols algebra ⋮ On projective modules over finite quantum groups ⋮ Poisson orders on large quantum groups ⋮ Braided racks, Hurwitz actions and Nichols algebras with many cubic relations. ⋮ Centralizing the centralizers ⋮ On Neeman’s gradient flows ⋮ EXAMPLES OF POINTED COLOR HOPF ALGEBRAS ⋮ Tensor Products of Modules Over a Certain Class of Quantum Doubles ⋮ On finite dimensional Nichols algebras of diagonal type ⋮ Equitable presentations for multiparameter quantum groups ⋮ The R-matrix of quantum doubles of Nichols algebras of diagonal type ⋮ Mixed vs stable anti-Yetter-Drinfeld contramodules ⋮ Representations of U¯qsℓ(2|1) at even roots of unity ⋮ Finite-dimensional Nichols algebras over dual Radford algebras ⋮ Typical irreducible characters of generalized quantum groups ⋮ On Hopf algebras with triangular decomposition ⋮ Pointed Hopf algebras -- from enveloping algebras to quantum groups and beyond. ⋮ From Hopf Algebras to Tensor Categories ⋮ Virasoro Central Charges for Nichols Algebras ⋮ Twisted deformations vs. cocycle deformations for quantum groups ⋮ Multiparameter quantum groups at roots of unity ⋮ On finite GK-dimensional Nichols algebras over abelian groups ⋮ Representations of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one.

Cites Work

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