Poisson structures on moduli spaces of representations
Poisson structures on moduli spaces of representations
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DOI：
10.1016/j.jalgebra.2010.09.033
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发表时间：
2011
影响因子：
0.9
通讯作者：
W. Crawley-Boevey
中科院分区：
文献类型：
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作者：
W. Crawley-Boevey
我们表明，泊松结构可以诱导仿射模空间的（半单）表示的结合代数从一个合适的李代数结构上的零Hochschild同调的代数。特别是这适用于项链李代数的道路代数的双重箭图和预投射代数。我们称这样的结构为H 0-Poisson结构，并证明了它们在Azumaya代数和Morita等价下是良好的。
We show that a Poisson structure can be induced on the affine moduli space of (semisimple) representations of an associative algebra from a suitable Lie algebra structure on the zeroth Hochschild homology of the algebra. In particular this applies to necklace Lie algebra for path algebras of doubled quivers and preprojective algebras. We call such structures H0-Poisson structures, and show that they are well behaved for Azumaya algebras and under Morita equivalence.