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. London Math Soc Stud Texts, 65. Cambridge: Cambridge University Press, 2005

[2] Auslander M, Reiten I, Smalϕ S O. Representation Theory of Artin Algebras. Cambridge Stud Adv Math, 36. Cambridge: Cambridge University Press, 1995

[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

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg