Rank 2 Nichols algebras with finite arithmetic root system
  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 
I. Heckenberger