Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type | Zendy

Qian Chen | Zendy; Jing Wang | Zendy

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Finite Cartan Graphs Attached to Nichols Algebras of Diagonal Type

Author(s) -

Qian Chen,

Jing Wang

Publication year - 2021

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2021/8129361

Subject(s) - diagonal , rank (graph theory) , type (biology) , mathematics , cartan matrix , pure mathematics , hopf algebra , algebra over a field , combinatorics , non associative algebra , universal enveloping algebra , geometry , ecology , biology

Nichols algebras are fundamental objects in the construction of quantized enveloping algebras and in the classification of pointed Hopf algebras by the lifting method of Andruskiewitsch and Schneider. The structure of Cartan graphs can be attached to any Nichols algebras of diagonal type and plays an important role in the classification of Nichols algebras of diagonal type with a finite root system. In this paper, the main properties of all simply connected Cartan graphs attached to rank 6 Nichols algebras of diagonal type are determined. As an application, we obtain a subclass of rank 6 finite dimensional Nichols algebras of diagonal type.

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