A Hopf algebra quantizing a necklace Lie algebra canonically associated to a quiver

Details A Hopf algebra quantizing a necklace Lie algebra canonically associated to a quiver A Hopf algebra quantizing a necklace Lie algebra canonically associated to a quiver

2004-06-09

arxiv.org/abs/math/0406200v2

Mathematics

Quantum Algebra

23 pages, 11 figures, AMSLaTeX; revised version corrects S^2 = Id and includes representations

Scientific paper

V. Ginzburg, and independently R. Bocklandt and L. Le Bruyn, defined an infinite-dimensional "necklace" Lie algebra canonically associated to any quiver. Following suggestions of V. Turaev, P. Etingof, and Ginzburg, we define a cobracket and prove that it defines a Lie bialgebra structure. We then present a Hopf algebra quantizing this Lie bialgebra, and prove that it is a Hopf algebra satisfying the PBW property. We present representations into spaces of differential operators on representations of the quiver, which quantize the trace representations of the Lie algebra given by Ginzburg.

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