Character groups of hopf algebras as infinite-dimensional lie groups
Journal article, 2016

In this article character groups of Hopf algebras are studied from the perspective of infinite-dimensional Lie theory. For a graded and connected Hopf algebra we obtain an infinite-dimensional Lie group structure on the character group with values in a locally convex algebra. This structure turns the character group into a Baker-Campbell-Hausdorff-Lie group which is regular in the sense of Milnor. Furthermore, we show that certain subgroups associated to Hopf ideals become closed Lie subgroups of the character group. If the Hopf algebra is not graded, its character group will in general not be a Lie group. However, we show that for any Hopf algebra the character group with values in a weakly complete algebra is a pro-Lie group in the sense of Hofmann and Morris.

Infinite-dimensional Lie group

Pro-Lie group

Butcher group

Continuous inverse algebra

Weakly complete space

Hopf algebra

Real analytic


Geir Bogfjellmo

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Rafael Dahmen

Technische Universität Darmstadt

Alexander Schmeding

Norwegian University of Science and Technology (NTNU)

Annales de lInstitut Fourier

0373-0956 (ISSN)

Vol. 66 5 2101-2155

Subject Categories

Mathematical Analysis



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