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Journal of Lie Theory 28 (2018), No. 2, 309--322
Copyright Heldermann Verlag 2018

Poisson Centralizer of the Trace

Szabolcs Mészáros
Dept. of Mathematics, Central European University, Nador u. 9, Budapest 1051, Hungary

The Poisson centralizer of the i-th trace element is determined in the coordinate ring of SLn endowed with the Poisson structure obtained as the semiclassical limit of its quantized coordinate ring. It turns out that this maximal Poisson-commutative subalgebra coincides with the subalgebra of invariants with respect to the adjoint action.

Keywords: Quantized coordinate ring, semiclassical limit, Poisson algebra, complete involutive system, maximal Poisson-commutative subalgebra.

MSC: 16T20, 17B63; 16W70, 20G42

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