Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type

DOI10.1016/j.jalgebra.2010.02.013zbMath1238.17010arXiv0710.4521OpenAlexW2962838237MaRDI QIDQ965195

István Heckenberger

Publication date: 21 April 2010

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

Full work available at URL: https://arxiv.org/abs/0710.4521

zbMATH Keywords

quantum groupHopf algebraWeyl groupoid

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Ring-theoretic aspects of quantum groups (16T20)

Related Items (32)

Nichols systems and their reflections ⋮ Distinguished pre-Nichols algebras ⋮ Algebras of non-local screenings and diagonal Nichols algebras ⋮ Simple modules of the quantum double of the Nichols algebra of unidentified diagonal type 𝔲𝔣𝔬(7) ⋮ Pointed Hopf actions on central simple division algebras ⋮ Finite GK-dimensional pre-Nichols algebras of super and standard type ⋮ Centers of generalized quantum groups ⋮ Poisson orders on large quantum groups ⋮ On defining ideals and differential algebras of Nichols algebras. ⋮ Non-symmetrizable quantum groups: defining ideals and specialization ⋮ Modified graded Hennings invariants from unrolled quantum groups and modified integral ⋮ Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras ⋮ EXAMPLES OF POINTED COLOR HOPF ALGEBRAS ⋮ Combinatorial Yang-Baxter maps arising from the tetrahedron equation ⋮ Nichols algebras over weak Hopf algebras ⋮ On finite dimensional Nichols algebras of diagonal type ⋮ Equitable presentations for multiparameter quantum groups ⋮ A simplicial complex of Nichols algebras ⋮ The unrolled quantum group inside Lusztig's quantum group of divided powers ⋮ The R-matrix of quantum doubles of Nichols algebras of diagonal type ⋮ LUSZTIG SYMMETRIES AND AUTOMORPHISMS OF QUANTUM SUPERALGEBRAS U_q(osp(1|2r)) ⋮ On unrolled Hopf algebras ⋮ Finite GK-dimensional pre-Nichols algebras of quantum linear spaces and of Cartan type ⋮ Symmetric pairs for Nichols algebras of diagonal type via star products ⋮ Kostant-Lusztig 𝔸-bases of multiparameter quantum groups ⋮ Typical irreducible characters of generalized quantum groups ⋮ On Hopf algebras with triangular decomposition ⋮ Two-parameter quantum affine algebra of type G2(1), Drinfeld realization and vertex representation ⋮ From Hopf Algebras to Tensor Categories ⋮ Classification of finite-dimensional irreducible representations of generalized quantum groups via Weyl groupoids ⋮ Twisted deformations vs. cocycle deformations for quantum groups ⋮ Multiparameter quantum groups at roots of unity

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