|
|
Poisson structures on basic cycles |
Yanhong BAO1,2, Xianneng DU1, Yu YE2() |
1. School of Mathematical Sciences, Anhui University, Hefei 230601, China; 2. Department of Mathematics, University of Science and Technology of China, Hefei 230036, China |
|
|
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
|
Corresponding Author(s):
YE Yu,Email:yeyu@ustc.edu.cn
|
Issue Date: 01 June 2012
|
|
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, Smal? S O. Representation Theory of Artin Algebras. Cambridge Stud Adv Math , 36. Cambridge: Cambridge University Press, 1995 doi: 10.1017/CBO9780511623608
|
3 |
Casasa J M, Datuashvilib T. Noncommutative Leibniz-Poisson algebras. Commun Algebra , 2006, 34: 2507-2530 doi: 10.1080/00927870600651091
|
4 |
Crawley-Boevey W. Poisson structures on moduli spaces of representations. J Algebra , 2011, 325: 205-215 doi: 10.1016/j.jalgebra.2010.09.033
|
5 |
Flato M, Gerstenhaber M, Voronow A A. Cohomology and deformation of Leibniz pairs. Lett Math Phys , 1995, 34: 77-90 doi: 10.1007/BF00739377
|
6 |
Farkas D, Letzter G. Ring theory from symplectic geometry. J Pure Appl Algebra , 1998, 125: 155-190 doi: 10.1016/S0022-4049(96)00117-X
|
7 |
Kubo F. Finite-dimensional non-commutative Poisson algebras. J Pure Appl Algebra , 1996, 113: 307-314 doi: 10.1016/0022-4049(95)00151-4
|
8 |
Kubo F. Non-commutative Poisson algebra structures on affine Kac-Moody algebras. J Pure Appl Algebra , 1998, 126: 267-286 doi: 10.1016/S0022-4049(96)00141-7
|
9 |
Van den Bergh M. Double Poisson algebras. Trans Amer Math Soc , 2008, 360: 5711-5769 doi: 10.1090/S0002-9947-08-04518-2
|
10 |
Xu P. Noncommutative Poisson algebras. Amer J Math , 1994, 116(1): 101-125 doi: 10.2307/2374983
|
11 |
Yao Y, Ye Y, Zhang P. Quiver Poisson algebras. J Algebra , 2007, 312: 570-589 doi: 10.1016/j.jalgebra.2007.03.034
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
|
Shared |
|
|
|
|
|
Discussed |
|
|
|
|