nLab necklace Lie algebra

A necklace in a quiver is a closed oriented path in the quiver up to cyclic permutation of the arrows making up the cycle. The space of necklaces in the path algebra of a quiver has a natural Lie algebra structure, which is a noncommutative analogue of a Poisson bracket on the sympletic reduction. In the case of one vertex and n loops the path algebra is the free associative algebra on n generators. In that case the necklace Lie algebra is introduced in

Quantization of the necklace Lie bialgebra

  • Victor Ginzburg, Travis Schedler, Moyal quantization of necklace Lie algebras, arXiv:0503405
  • T. Schedler, A Hopf algebra quantizing a necklace Lie algebra canonically associated to a quiver, Int. Math. Res. Not. 2005 (12) (2005) 725–760
category: algebra

Last revised on October 12, 2022 at 11:03:21. See the history of this page for a list of all contributions to it.