共查询到20条相似文献,搜索用时 0 毫秒
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在交换环R上,引入了Clean-正合以及Clean-导出范畴的概念,分别给出了Clean-短正合列和Clean-正合复形的等价刻画,研究了Clean-导出范畴的性质.特别地,证明了有界Clean-导出范畴可以实现为特殊的同伦范畴. 相似文献
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We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These categories naturally fit into a framework of relative derived categories, and once we prove that there are decent resolutions of complexes, we are able to prove many familiar results in homological algebra. 相似文献
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《代数通讯》2013,41(9):3195-3223
ABSTRACT In this article, we develop the obstruction theory for lifting complexes, up to quasi-isomorphism, to derived categories of flat nilpotent deformations of abelian categories. As a particular case we also obtain the corresponding obstruction theory for lifting of objects in terms of Yoneda Ext-groups. In an appendix we prove the existence of miniversal derived deformations of complexes. 相似文献
7.
Liangyu Chen & Lin Xin 《数学研究》2015,48(4):406-418
In this paper, we study a class of $P$-semi-abelian categories, as well as left
and right cohomological functors. Then we establish the corresponding one-side derived
categories. 相似文献
8.
We establish an algebra-isomorphism between the complexified Grothendieck ring of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces
of those bimodule categories. This provides a purely categorical proof of a conjecture by Ostrik concerning the structure
of . As a by-product we obtain a concrete expression for the structure constants of the Grothendieck ring of the bimodule category
in terms of endomorphisms of the tensor unit of the underlying modular tensor category.
相似文献
9.
It is well-known that if R is a left Noetherian ring, then there is a bijective correspondence between minimal prime ideals of R and maximal torsion radicals of R-Mod. Using the notion of a prime M-ideal, it is shown that this correspondence can be extended to the category σ[M] of modules subgenerated by a module M, provided that M is a Noetherian quasi-projective generator in σ[M]. Furthermore, under this hypothesis the prime M-ideals are the fully invariant submodules P of M such that M/P is semi-compressible. 相似文献
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Qunhua Liu 《代数通讯》2013,41(12):5080-5093
We explicitly describe all spherical objects, as well as tilting objects, of the multiplicity free Brauer tree algebra with two edges. 相似文献
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The finite dimensional tame hereditary algebras are associated with the extended Dynkin diagrams. An indecomposable module over such an algebra is either preprojective or preinjective or lies in a family of tubes whose tubular type is the corresponding Dynkin diagram. The study of one-point extensions by simple regular modules in such tubes was initiated in [Ri]. We generalise this approach by starting out with algebras which are derived equivalent to a tame hereditary algebra and considering one-point extensions by modules which are simple regular in tubes in the derived category. If the obtained tubular type is again a Dynkin diagram these algebras are called derived Dynkin extensions. Our main theorem says that a representation infinite algebra is derived equivalent to a tame hereditary algebra iff it is an iterated derived Dynkin extension of a tame concealed algebra. As application we get a new proof of a theorem in [AS] about domestic tubular branch enlargements which uses the derived category instead of combinatorial arguments. 相似文献
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Aderemi Kuku 《K-Theory》2001,22(4):367-392
Let
be a rational prime,
an exact category. In this article, we define and study for all
, the profinite higher K-theory of
, that is
as well as
, where
is the
-dimensional mod-
Moore space. We study connections between
and prove several
-completeness results involving these and associated groups including the cases where
is the category of finitely generated (resp. finitely generated projective) modules over orders in semi-simple algebras over number fields and p-adic fields. We also define and study continuous K-theory
of orders in p-adic semi-simple algebras and show some connection between the profinite and continuous K-theory of . 相似文献
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Marco A. Farinati 《Algebras and Representation Theory》2003,6(3):303-331
We study the derived invariance of the cohomology theories Hoch
*, H
* and HC
* associated with coalgebras over a field. We prove a theorem characterizing derived equivalences. As particular cases, it describes the two following situations: (1) f: CD a quasi-isomorphism of differential graded coalgebras, (2) the existence of a cotilting bicomodule
C
T
D
. In these two cases we construct a derived-Morita equivalence context, and consequently we obtain isomorphisms Hoch
*(C)Hoch
*(D) and H
*(C)H
*(D). Moreover, when we have a coassociative map inducing an isomorphism H
*(C)H
*(D) (for example, when there is a quasi-isomorphism f: CD), we prove that HC
*(C)HC
*(D). 相似文献
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We give a complete derived equivalence classification of all nonstandard representation-infinite domestic selfinjective algebras over an algebraically closed field. As a consequence, a complete stable equivalence classification of these algebras is obtained. 相似文献
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Lukáš Vokřínek 《代数通讯》2013,41(5):2110-2117
We provide a counterexample to a theorem of Ford, namely a pushout square of categories with all involved functors injective, such that there is no associated exact “Mayer–Vietoris” sequence of derived limits. Further, we construct a Mayer–Vietoris sequence for derived (co)limits under some additional hypotheses, extending the well-known case of a pushout square of group monomorphisms. 相似文献
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In this paper, we present some results on the bounded derived category of Artin algebras, and in particular on the indecomposable
objects in these categories, using homological properties. Given a complex X
*, we consider the set and we define the application . We give relationships between some homological properties of an algebra and the respective application l. On the other hand, using homological properties again, we determine two subcategories of the bounded derived category of
an algebra, which turn out to be the bounded derived categories of quasi-tilted algebras. As a consequence of these results
we obtain new characterizations of quasi-tilted and quasi-tilted gentle algebras.
Presented by Raymundo Bautista. 相似文献
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We establish sufficient conditions for a biextension algebra of a piecewise hereditary algebra of type n or Dn by indecomposable modules of derived regular length 2 to be of tame representation type. 相似文献
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We generalize the constructions of layered domains? to layered semirings, in order to enrich the structure, and in particular to provide finite examples for applications in arithmetic. The layered category theory is extended accordingly, to cover noncancellative monoids, which are examined in their own right. 相似文献
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Boris Youssin 《K-Theory》1997,11(4):373-395
We define the notion of cobordism of two objects in a trianulated category, and the Witt group of such category is defined as the Grothendieck group of cobordism classes of self-dual objects. We prove that the Witt group of a t-category is a free Abelian group generated by the classes of irreducible self-dual objects of its heart. In case of derived category of of complexes of sheaves on a stratified space with the middle-perversity t-structure, these irreducibles are local systems on the strata. 相似文献
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We consider smooth algebraic varieties with ample either canonical or anticanonical sheaf. We prove that such a variety is uniquely determined by its derived category of coherent sheaves. We also calculate the group of exact autoequivalences for these categories. The technics of ample sequences in Abelian categories is used. 相似文献