Poisson structures on basic cycles

Abstract

The Poisson structures on a basic cycle are determined completely via quiver techniques. As a consequence, all Poisson structures on basic cycles are inner.

Keywords

Poisson algebra / inner Poisson structure / basic cycle

References

[1] Assem I., Simson D., Skowronski A. Elements of the Representations Theory of Associative Algebras, 2005, Cambridge: Cambridge University Press

[2] Auslander M., Reiten I., Smalϕ S. O. Representation Theory of Artin Algebras, 1995, Cambridge: Cambridge University Press

[3] Casasa J. M., Datuashvilib T. Noncommutative Leibniz-Poisson algebras. Commun Algebra, 2006, 34: 2507-2530

[4] Crawley-Boevey W. Poisson structures on moduli spaces of representations. J Algebra, 2011, 325: 205-215

[5] Flato M., Gerstenhaber M., Voronow A. A. Cohomology and deformation of Leibniz pairs. Lett Math Phys, 1995, 34: 77-90

[6] Farkas D., Letzter G. Ring theory from symplectic geometry. J Pure Appl Algebra, 1998, 125: 155-190

[7] Kubo F. Finite-dimensional non-commutative Poisson algebras. J Pure Appl Algebra, 1996, 113: 307-314

[8] Kubo F. Non-commutative Poisson algebra structures on affine Kac-Moody algebras. J Pure Appl Algebra, 1998, 126: 267-286

[9] Van den Bergh M. Double Poisson algebras. Trans Amer Math Soc, 2008, 360: 5711-5769

[10] Xu P. Noncommutative Poisson algebras. Amer J Math, 1994, 116(1): 101-125

[11] Yao Y., Ye Y., Zhang P. Quiver Poisson algebras. J Algebra, 2007, 312: 570-589