An Equivalence of Categories for Lie Color Algebras

Abstract

Let k be a field with char k = p > 0 and G an abelian group with a bicharacter λ on G. For each p-(G,λ)-Lie color algebra L over k the p-universal enveloping algebra u(L) is a G-graded Hopf algebra,i.e.,a Hopf algebra in the category ^kG ℳ of kG-comodules. In this paper we describe a subcategory of ^kG ℳ which is equivalent to the category of the finite dimensional p-(G,λ)-Lie color algebras over k.

Key Words:

• Lie color algebra
• Universal enveloping algebra

Acknowledgments

The author would like to thank Prof. Dr. H.-J. Schneider from the University of Munich for many helpful discussions. This research was supported by the Graduiertenkolleg “Mathematik im Bereich ihrer Wechselwirkung mit der Physik” at the University of Munich.