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

2004/02/22 by I. Heckenberger, Heckenberger, I.
Mathematics · Physics and Astronomy · #16W35 #17B37 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/0402350

openalex publication_date 2004/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• Differential calculus on compact matrix pseudogroups (quantum groups)

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