COMPONENTWISE LINEAR MODULES OVER A KOSZUL ALGEBRA
نویسندگان
چکیده
منابع مشابه
Componentwise Linear Modules over a Koszul Algebra
In this paper we devote to generalizing some results of componentwise linear modules over a polynomial ring to the ones over a Koszul algebra. Among other things, we show that the i-linear strand of the minimal free resolution of a componentwise linear module is the minimal free resolution of some module which is described explicitly for any i ∈ Z. In addition we present some theorems about whe...
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We prove that every module over a commutative homogeneous Koszul algebra has regularity bounded by its regularity over a polynomial ring of which the Koszul algebra is a homomorphic image. From this we derive a result conjectured by George Kempf to the effect that a suffkiently high truncation of any module over a homogeneous Koszul algebra has a linear free resolution. ‘E’ 1992 Academic Press....
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Let G be a compact Lie group. Set Λ• = H∗(G) and S • = H(BG). The coefficients are in R or C. Suppose G acts on a reasonable space X. In the paper [GKM] Goresky, Kottwitz and MacPherson established a duality between the ordinary cohomology which is a module over Λ• and equivariant cohomology which is a module over S • . This duality is on the level of chains, not on the level of cohomology. The...
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Let g be a reductive Lie algebra over a field of characteristic zero. Suppose that g acts on a complex of vector spaces M by iλ and Lλ, which satisfy the same identities that contraction and Lie derivative do for differential forms. Out of this data one defines the cohomology of the invariants and the equivariant cohomology of M. We establish Koszul duality between them.
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Perturbation bounds in numerical linear algebra are traditionally derived and expressed using norms. Norm bounds cannot reflect the scaling or sparsity of a problem and its perturbation, and so can be unduly weak. If the problem data and its perturbation are measured componentwise, much smaller and more revealing bounds can be obtained. A survey is given of componentwise perturbation theory in ...
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ژورنال
عنوان ژورنال: Taiwanese Journal of Mathematics
سال: 2013
ISSN: 1027-5487
DOI: 10.11650/tjm.17.2013.3040