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Axioms 2012, 1(3), 259-290; doi:10.3390/axioms1030259

The Sum of a Finite Group of Weights of a Hopf Algebra

Department of Mathematics and Department of Statistics, Stanford University, 390 Serra Mall, Stanford, CA 94305, USA
Received: 2 July 2012 / Revised: 17 September 2012 / Accepted: 17 September 2012 / Published: 5 October 2012
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations)
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Abstract

Motivated by the orthogonality relations for irreducible characters of a finite group, we evaluate the sum of a finite group of linear characters of a Hopf algebra, at all grouplike and skew-primitive elements. We then discuss results for products of skew-primitive elements. Examples include groups, (quantum groups over) Lie algebras, the small quantum groups of Lusztig, and their variations (by Andruskiewitsch and Schneider).
Keywords: Hopf algebra; weights; grouplike; skew-primitive Hopf algebra; weights; grouplike; skew-primitive
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Khare, A. The Sum of a Finite Group of Weights of a Hopf Algebra. Axioms 2012, 1, 259-290.

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