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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.