Properties of pointed and connected Hopf algebras of finite Gelfand–Kirillov dimension | Zendy

Zhuang Guangbin | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Properties of pointed and connected Hopf algebras of finite Gelfand–Kirillov dimension

Author(s) -

Zhuang Guangbin

Publication year - 2013

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/jds079

Subject(s) - hopf algebra , mathematics , dimension (graph theory) , algebraically closed field , pure mathematics , integer (computer science) , representation theory of hopf algebras , division algebra , quasitriangular hopf algebra , algebra over a field , field (mathematics) , infinity , algebra representation , mathematical analysis , computer science , programming language

Let H be a pointed Hopf algebra. We show that under some mild assumptions H and its associated graded Hopf algebra gr H have the same Gelfand–Kirillov dimension (GK‐dimension). As an application, we prove that the GK‐dimension of a connected Hopf algebra is either infinity or a positive integer. We also classify connected Hopf algebras of GK‐dimension 3 over an algebraically closed field of characteristic 0.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research