Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 2, pp. 303-308 (2003)

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The Gelfand-Kirillov dimension of rings with Hopf algebra action

Thomas Guédénon

152, boulevard du Général Jacques, 1050 Bruxelles, Belgique; e-mail:

Abstract: Let $k$ be a perfect field, $H$ a irreducible cocommutative Hopf $k$-algebra and $P(H)$ the space of primitive elements of $H$, $R$ a $k$-algebra on which acts locally finitely $H$ and $R\#H$ the associated smash product. Assume that $H$ is almost solvable with $P(H)$ finite-dimensional $n$ and the sequences of divided powers are all infinite. Then the Gelfand-Kirillov dimension of $R\#H$ is $GK(R)+n$.

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Electronic version published on: 1 Aug 2003. This page was last modified: 4 May 2006.

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