A q-analogue of the dual space to the Lie algebras gl(2) and sl(2)

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, , Citation B A Kupershmidt 1993 J. Phys. A: Math. Gen. 26 L1 DOI 10.1088/0305-4470/26/1/001

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1 Tennessee Univ. Space Inst., Tullahoma, TN, USA

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Abstract

For the Lie group GL(n), the linear Poisson bracket on the dual space gl(n)* to the Lie algebra gl(n) is quadratically deformed to make the coadjoint action of GL(n) into a Poisson action, for arbitrary quadratic Poisson Lie structure on GL(n). For the case n=2, these formulae are quantized for both quantum groups GLq(2) and SLq(2).

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