Rank 2 Nichols algebras with finite arithmetic root system

Details Rank 2 Nichols algebras with finite arithmetic root system Rank 2 Nichols algebras with finite arithmetic root system

2004-12-22

arxiv.org/abs/math/0412458v1

Mathematics

Quantum Algebra

LaTeX2e, 21 pages

Scientific paper

The concept of arithmetic root systems is introduced. It is shown that there is a one-to-one correspondence between arithmetic root systems and Nichols algebras of diagonal type having a finite set of (restricted) Poincare'-Birkhoff-Witt generators. This has strong consequences for both objects. As an application all rank 2 Nichols algebras of diagonal type having a finite set of (restricted) Poincare'-Birkhoff-Witt generators are determined. Key Words: Brandt groupoid, Hopf algebra, pseudo-reflections, Weyl group

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