Nichols algebras of group type with many quadratic relations

Abstract

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over nonabelian groups satisfying an inequality for the dimension of the homogeneous subspace of degree two. All such Nichols algebras are finite-dimensional, and all known finite-dimensional Nichols algebras of nonabelian group type appear in the result of our classification. We find a new finite-dimensional Nichols algebra over fields of characteristic two.

arXiv comment29 pages

References in corpus (3)

• The Weyl-Brandt groupoid of a Nichols algebra of diagonal type
• Finite dimensional pointed Hopf algebras over S_4
• Non-unitary set-theoretical solutions to the Quantum Yang-Baxter Equation

Cited by in corpus (24)

• On structure groups of set-theoretic solutions to the Yang-Baxter equation
• The Nichols algebra of screenings
• On the classification of quandles of low order
• The classification of Nichols algebras over groups with finite root system of rank two
• Nichols algebras associated to the transpositions of the symmetric group are twist-equivalent
• Finite dimensional Hopf algebras over Kac-Paljutkin algebra $H_8$
• Braided racks, Hurwitz actions and Nichols algebras with many cubic relations
• A combinatorial approach to noninvolutive set-theoretic solutions of the Yang-Baxter equation
• Nichols algebras over groups with finite root system of rank two II
• An explicit description of the second cohomology group of a quandle
• Nichols algebras with many cubic relations
• Fusion in the entwined category of Yetter--Drinfeld modules of a rank-1 Nichols algebra
• Nichols algebras over groups with finite root system of rank two III
• A Universal algebraic approach to rack coverings
• New Large-Rank Nichols Algebras Over Nonabelian Groups With Commutator Subgroup Z_2
• Finite-dimensional Nichols algebras of simple Yetter-Drinfeld modules (over groups) of prime dimension
• Multinomial expansion and Nichols algebras associated to non-degenerate involutive solutions of the Yang-Baxter equation
• Coverings of graded pointed Hopf algebras
• Factorization of Graded Traces on Nichols Algebras
• Hurwitz Orbits with a Cellular Automaton
• Algebraic Properties of Quandle Extensions and Values of Cocycle Knot Invariants
• Generalized nil-Coxeter algebras over discrete complex reflection groups
• Divisibility Relations for the Dimensions and Hilbert series of Nichols Algebras of Non-Abelian Group Type
• Nichols algebras over classical Weyl groups, Fomin-Kirillov algebras and Lyndon basis