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Rank 2 Nichols algebras with finite arithmetic root system
I. Heckenberger
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 ha…
Weyl equivalence for rank 2 Nichols algebras of diagonal type
I. Heckenberger
Yetter--Drinfel'd modules of diagonal type admit an equivalence relation which conjecturally preserves dimension and Gel'fand--Kirillov dimension of the corresponding Nichols algeb…
The Weyl-Brandt groupoid of a Nichols algebra of diagonal type
I. Heckenberger
The theory of Nichols algebras of diagonal type is known to be closely related to that of semisimple Lie algebras. In this paper the connection between both theories is made closer…
Finite dimensional rank 2 Nichols algebras of diagonal type II: Classification
I. Heckenberger
The method of subquotients is developed and used to determine all finite dimensional rank 2 Nichols algebras of diagonal type over an arbitrary field of characteristic zero. Key Wo…
Finite dimensional rank 2 Nichols algebras of diagonal type I: Examples
I. Heckenberger
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 di…