Rigidity of truncated quiver algebras
نویسندگان
چکیده
منابع مشابه
The Cohomology Ring of Truncated Quiver Algebras
In this paper we determine the ring structure of the Hochschild cohomology of truncated quiver algebras with the Yoneda product. On the one hand Locateli described the cohomology groups in terms of classes of pairs of paths using minimal resolutions. On the other hand, the Yoneda product has a nice description on the bar resolution as the usual cup product. Our first main result is the explicit...
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For a truncated quiver algebra over a field of arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles. MSC(2000): 16E40, 16E10, 16G10
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A main contribution of this paper is the explicit construction of comparison morphisms between the standard bar resolution and Bardzell’s minimal resolution for truncated quiver algebras (TQA’s). As a direct application we describe explicitely the Yoneda product and derive several results on the structure of the cohomology ring of TQA’s. For instance, we show that the product of odd degree coho...
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These notes contain an extended abstract and references for a minicourse given at the Summer School ‘Microlocal and Geometric Methods in Representation Theory’ (Schloss Reisensburg, July 2006) of the International Research Training Group Metz–Paderborn.
متن کاملQuiver Schur Algebras for the Linear Quiver I
We define a graded quasi-hereditary covering for the cyclotomic quiver Hecke algebras Rn of type A when e = 0 (the linear quiver) or e ≥ n. We show that these algebras are quasi-hereditary graded cellular algebras by giving explicit homogeneous bases for them. When e = 0 we show that the KLR grading on the quiver Hecke algebras is compatible with the gradings on parabolic category OΛ n previous...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1990
ISSN: 0001-8708
DOI: 10.1016/0001-8708(90)90057-t