Modulation and natural valued quiver of an algebra
نویسندگان
چکیده
منابع مشابه
Homological algebra of quiver bundles
The category of representations of a finite quiver in the category of sheaves of modules on a ringed space is abelian. We show that this category has enough injectives by constructing an explicit injective resolution. From this resolution we deduce a long exact sequence relating the Ext groups in these two categories. We also show that under some hypotheses, the Ext groups are isomorphic to cer...
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Quivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or preprojective algebra. In the current paper, we study these objects in detail. We show that the quiver grassmannians corresponding to submodules of certain injective ...
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Using a result of T. P. Bidigare [Bidigare, 1997], we identity the descent algebra Σk(W ) (over a field k) of a finite Coxeter group W with a subalgebra of kF , an algebra built from the hyperplane arrangement associated to W . Specifically, Σk(W ) is anti-isomorphic to the W -invariant subalgebra (kF) . We use this identification and results about kF to study Σk(W ). We construct a complete sy...
متن کاملThe Hall Algebra of a Cyclic Quiver
We show that the generic Hall algebra of nilpotent representations of an oriented cycle specialised at q = 0 is isomorphic to the generic extension monoid in the sense of Reineke. This continues the work of Reineke in [3]. 1. The generic extension monoid and the generic Hall algebra For the following let Q be a finite quiver with vertex set Q0 and arrow set Q1. We consider only finite dimension...
متن کاملHomological algebra of twisted quiver bundles
Several important cases of vector bundles with extra structure (such as Higgs bundles and triples) may be regarded as examples of twisted representations of a finite quiver in the category of sheaves of modules on a variety/manifold/ringed space. We show that the category of such representations is an abelian category with enough injectives by constructing an explicit injective resolution. Usin...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2012
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.2012.256.105