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Given a maximal rigid object T of the cluster tube, we determine the objects finitely presented by T. We then use the method of Keller and Reiten to show that the endomorphism algebra of T is Gorenstein and of finite representation type, as first shown by Vatne. This algebra turns out to be the Jacobian algebra of a certain quiver with potential, when the characteristic of the base field is not 3. We study how this quiver with potential changes when T is mutated. We also provide a derived equivalence classification for the endomorphism algebras of maximal rigid objects. 相似文献
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本文研究了2-Calabi-Yau三角范畴上的2-Calabi-Yau tilted代数的almost complete tilting模.我们利用2-Calabi-Yau三角范畴上的交换关系给出了2-Calabi-Yau tilted代数的almost complete tilting模有两个(Bongartz)补的一系列充分必要条件. 相似文献
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The construction of free R-modules over a Cartesian closed topological category X is detailed (where R is a ring object in X), and it is shown that the insertion of generators is an embedding. This result extends the well-known construction of free groups, and more generally of free algebras over a Cartesian closed topological category.
Mathematics Subject Classifications (2000) 18D15, 18D35, 18A40. 相似文献
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Claudio Schmidt-Wegenast 《代数通讯》2013,41(2):715-725
Let X be an indecomposable regular module over a connected wild hereditary path-algebra. The main result is a factorization property for maps in the radical of End H (X) and an upper bound for its degree of nilpotency. The bound is sharp if X has elementary quasi-top. In this, case the socle of End H (X) can also be characterized. 相似文献
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Algebras and Modules in Monoidal Model Categories 总被引:5,自引:0,他引:5
In recent years the theory of structured ring spectra (formerlyknown as A- and E-ring spectra) has been simplified by the discoveryof categories of spectra with strictly associative and commutativesmash products. Now a ring spectrum can simply be defined asa monoid with respect to the smash product in one of these newcategories of spectra. In this paper we provide a general methodfor constructing model category structures for categories ofring, algebra, and module spectra. This provides the necessaryinput for obtaining model categories of symmetric ring spectra,functors with smash product, Gamma-rings, and diagram ring spectra.Algebraic examples to which our methods apply include the stablemodule category over the group algebra of a finite group andunbounded chain complexes over a differential graded algebra.1991 Mathematics Subject Classification: primary 55U35; secondary18D10. 相似文献
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We construct a generalization of the BGG-category O, whose blocks correspond to standardly stratified algebras. We prove reciprocity formulae in these categories and present two classes of examples. 相似文献
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George Ciprian Modoi 《代数通讯》2013,41(3):995-1011
We say that a projective class in a triangulated category with coproducts is perfect if the corresponding ideal is closed under coproducts of maps. We study perfect projective classes and the associated phantom and cellular towers. Given a perfect generating projective class, we show that every object is isomorphic to the homotopy colimit of a cellular tower associated to that object. Using this result and the Neeman's Freyd-style representability theorem, we give a new proof of Brown Representability Theorem. 相似文献
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Crossed Modules and Quantum Groups in Braided Categories 总被引:2,自引:0,他引:2
Yu. N. Bespalov 《Applied Categorical Structures》1997,5(2):155-204
Let A be a Hopf algebra in a braided category
. Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category
of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group
the corresponding braided category of modules
is identified with a full subcategory in
. The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid–Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized. 相似文献
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Grzegorz BOBINSKI 《数学学报(英文版)》2007,23(6):1033-1052
The aim of the paper is to classify the indecomposable modules and describe the Auslander-Reiten sequences for the admissible algebras with formal two-ray modules. 相似文献
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本文我们研究了两类$W$-型李代数$g(\lambda)$的Verma模的结构. 在一定条件下,我们决定了这些Verma模的可约性及相应的奇异向量. 相似文献
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In this note we first show that if H is a finite-dimensional Hopf algebra in a group Yetter-Drinfel'd category L^LyD(π) over a crossed Hopf group-coalgebra L, then its dual H^* is also a Hopf algebra in the category L^LyD(π). Then we establish the fundamental theorem of Hopf modules for H in the category L^LyD(π). 相似文献
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