Finite dimensional Nichols algebras over finite cyclic groups

Abstract

All finite dimensional Nichols algebras with diagonal type of connected finite dimensional Yetter-Drinfeld modules over finite cyclic group ${\mathbb{Z}}_n$ are found. It is proved that finite dimensional Nichols algebra over ${\mathbb{Z}}_2$ is a quantum linear space and Nichols algebra of connected Yetter-Drinfeld module $V$ over ${\mathbb{Z}}_n$ with $\dim V>3$ is infinite dimensional.

22 pages, substantially shortened and reference added. Version to appear in Journal of Lie Theory

References in corpus (3)

• The Weyl-Brandt groupoid of a Nichols algebra of diagonal type
• Finite dimensional rank 2 Nichols algebras of diagonal type I: Examples
• Rank 2 Nichols algebras with finite arithmetic root system

Cited by in corpus (1)

• On Fomin--Kirillov Algebras for Complex Reflection Groups