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On the centre of two-parameter quantum groups

Published online by Cambridge University Press:  30 July 2007

Georgia Benkart
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA (benkart@math.wisc.edu)
Seok-Jin Kang
Affiliation:
Department of Mathematical Sciences, Seoul National University, San 56-1 Shinrim–dong, Kwanak–ku, Seoul 151–747, Korea (sjkang@math.snu.ac.kr)
Kyu-Hwan Lee
Affiliation:
Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA (khlee@math.uconn.edu)

Abstract

We describe Poincaré–Birkhoff–Witt bases for the two-parameter quantum groups U = Ur,s(sln) following Kharchenko and show that the positive part of U has the structure of an iterated skew polynomial ring. We define an ad-invariant bilinear form on U, which plays an important role in the construction of central elements. We introduce an analogue of the Harish-Chandra homomorphism and use it to determine the centre of U.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2006

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