The Nichols algebra of a semisimple Yetter-Drinfeld module
From MaRDI portal
Publication:3066533
zbMath1214.16024arXiv0803.2430MaRDI QIDQ3066533
Nicolás Andruskiewitsch, István Heckenberger, Hans-Juergen Schneider
Publication date: 11 January 2011
Full work available at URL: https://arxiv.org/abs/0803.2430
Yetter-Drinfeld modulesfinite-dimensional Hopf algebrasreal rootspointed Hopf algebrasNichols algebrasWeyl groupoidsgeneralized Cartan matrices
Related Items
Distinguished pre-Nichols algebras ⋮ Algebras of non-local screenings and diagonal Nichols algebras ⋮ The classification of Nichols algebras over groups with finite root system of rank two ⋮ On nondiagonal finite quasi-quantum groups over finite abelian groups ⋮ Diagrams of Hopf algebras with the Chevalley property ⋮ Finite quasi-quantum groups over abelian groups ⋮ Finite dimensional Hopf algebras over Kac-Paljutkin algebra $H_8$ ⋮ Divisibility relations for the dimensions and Hilbert series of Nichols algebras of non-Abelian group type. ⋮ Right coideal subalgebras of Nichols algebras and the Duflo order on the Weyl groupoid. ⋮ Bruhat order and nil-Hecke algebras for Weyl groupoids ⋮ On projective modules over finite quantum groups ⋮ Rank 4 finite-dimensional Nichols algebras of diagonal type in positive characteristic ⋮ A presentation by generators and relations of Nichols algebras of diagonal type and convex orders on root systems. ⋮ Frieze patterns as root posets and affine triangulations ⋮ Finite-dimensional pointed or copointed Hopf algebras over affine racks. ⋮ New large-rank Nichols algebras over nonabelian groups with commutator subgroup \(\mathbb Z_2\). ⋮ Complete reducibility theorems for modules over pointed Hopf algebras. ⋮ Rank 4 Nichols algebras of pale braidings ⋮ Pointed Hopf algebras over the sporadic simple groups. ⋮ Duality for infinite-dimensional braided bialgebras and their (co)modules ⋮ On Hopf algebras over basic Hopf algebras of dimension 24 ⋮ Simple modules of small quantum groups at dihedral groups ⋮ Quasi-triangular Hopf algebras and invariant Jacobians ⋮ Braided racks, Hurwitz actions and Nichols algebras with many cubic relations. ⋮ Finite-dimensional pointed Hopf algebras over \(\mathbb S_4\). ⋮ On Nichols algebras over basic Hopf algebras ⋮ Finite-dimensional Hopf algebras over the Hopf algebra \(H_{d:-1,1}\) of Kashina ⋮ Yetter-Drinfeld modules over bosonizations of dually paired Hopf algebras. ⋮ Strongly symmetric smooth toric varieties ⋮ Finite-dimensional Hopf algebras over the Hopf algebra \(H_{b:1}\) of Kashina ⋮ Quantum groups and Nichols algebras acting on conformal field theories ⋮ Nichols algebras over groups with finite root system of rank two. III. ⋮ Non-symmetrizable quantum groups: defining ideals and specialization ⋮ Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type. I: Non-semisimple classes in \(\mathbf{PSL}_n(q)\). ⋮ Nichols algebras that are quantum planes ⋮ Copointed Hopf algebras over \(\mathbb{S}_4\) ⋮ On finite dimensional Nichols algebras of diagonal type ⋮ Finite Cartan graphs attached to Nichols algebras of diagonal type ⋮ A classification of Nichols algebras of semisimple Yetter-Drinfeld modules over non-abelian groups ⋮ A simplicial complex of Nichols algebras ⋮ Rank three Nichols algebras of diagonal type over arbitrary fields ⋮ A bound for crystallographic arrangements ⋮ The unrolled quantum group inside Lusztig's quantum group of divided powers ⋮ Finite-dimensional pointed Hopf algebras with alternating groups are trivial. ⋮ Pointed Hopf algebras over some sporadic simple groups. ⋮ Factorization of graded traces on Nichols algebras ⋮ Representations of U¯qsℓ(2|1) at even roots of unity ⋮ PBW deformations of a Fomin-Kirillov algebra and other examples ⋮ On pointed Hopf algebras associated with the symmetric groups. ⋮ Weyl groupoids with at most three objects. ⋮ Double-bosonization and Majid's conjecture. II: Irregular \(R\)-matrices and type-crossing to \(G_2\) ⋮ On Hopf algebras over the unique 12-dimensional Hopf algebra without the dual Chevalley property ⋮ Finite-dimensional Nichols algebras over dual Radford algebras ⋮ On the Tits cone of a Weyl groupoid ⋮ Nonsemisimple Hopf algebras of dimension 8𝑝 with the Chevalley property ⋮ On Hopf algebras with triangular decomposition ⋮ Structures of Nichols (braided) Lie algebras of diagonal type ⋮ Classification of finite-dimensional Hopf algebras over dual Radford algebras ⋮ Virasoro Central Charges for Nichols Algebras ⋮ Partially dualized Hopf algebras have equivalent Yetter-Drinfel'd modules. ⋮ On finite GK-dimensional Nichols algebras over abelian groups ⋮ On some classification of finite-dimensional Hopf algebras over the Hopf algebra Hb:1* of Kashina ⋮ On the Lifting of Nichols Algebras
