Finite dimensional rank 2 Nichols algebras of diagonal type I: Examples

Abstract

Nichols algebras naturally appear in the classification of finite dimensional pointed Hopf algebras. Assuming only that the base field has characteristic zero several new finite dimensional rank 2 Nichols algebras of diagonal type are listed. Each of them is described in terms of generators and relations. A Poincaré--Birkhoff--Witt basis of all of these Nichols algebras is given and their dimension is computed. Together with the continuation of this paper this gives an answer to a question of Andruskiewitsch. Key Words: Hopf algebra, Lyndon words, full binary tree

Abstract and introduction modified, one example added; Latex2e, 36 pages, 24 figures

References in corpus (1)

• Some remarks on Nichols algebras

Cited by in corpus (5)

• The Weyl-Brandt groupoid of a Nichols algebra of diagonal type
• Finite dimensional rank 2 Nichols algebras of diagonal type II: Classification
• Weyl equivalence for rank 2 Nichols algebras of diagonal type
• Rank 2 Nichols algebras with finite arithmetic root system
• Finite dimensional Nichols algebras over finite cyclic groups