Frontiers of Mathematics in China >
Poisson structures on basic cycles
Received date: 17 Apr 2011
Accepted date: 10 Oct 2011
Published date: 01 Jun 2012
Copyright
The Poisson structures on a basic cycle are determined completely via quiver techniques. As a consequence, all Poisson structures on basic cycles are inner.
Key words： Poisson algebra; inner Poisson structure; basic cycle
Yanhong BAO , Xianneng DU , Yu YE . Poisson structures on basic cycles[J]. Frontiers of Mathematics in China, 2012 , 7(3) : 385 -396 . DOI: 10.1007/s11464-012-0174-9
| 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
|
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