Nichols algebras that are quantum planes

Abstract

We compute all Nichols algebras of rigid vector spaces of dimension 2 that admit a non-trivial quadratic relation.

arXiv comment29 pages

References in corpus (4)

• On Hopf Algebras over quantum subgroups
• Classification of the quantum deformation of the superalgebra $GL(1|1)$
• Duality for Exotic Bialgebras
• Duality and Representations for New Exotic Bialgebras

Cited by in corpus (11)

• Finite-dimensional Hopf algebras over the Hopf algebra $H_{b:1}$ of Kashina
• Finite-dimensional Hopf algebras over the smallest non-pointed basic Hopf algebra
• Finite dimensional Nichols algebras over Suzuki algebra I: simple Yetter-Drinfeld modules of $A_{N2n}^{\mu \lambda }$
• Finite-dimensional Nichols algebras over dual Radford algebras
• On Hopf algebras over the unique $12$-dimensional Hopf algebra without the dual Chevalley property
• On Hopf algebras over basic Hopf algebras of dimension 24
• Classification of finite-dimensional Hopf algebras over dual Radford algebras
• Finite dimensional Nichols algebras over Suzuki algebra II: over simple Yetter-Drinfeld modules of $A_{N2n+1}^{\mu \lambda }$
• The Nichols algebra $\mathfrak{B}(V_{abe})$ and a class of combinatorial numbers
• Multinomial expansion and Nichols algebras associated to non-degenerate involutive solutions of the Yang-Baxter equation
• On braided Hopf structures on exterior algebras