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131.
We systematically study noncommutative and nonassociative algebras and their bimodules as algebras and bimodules internal to the representation category of a quasitriangular quasi-Hopf algebra. We enlarge the morphisms of the monoidal category of -bimodules by internal homomorphisms, and describe explicitly their evaluation and composition morphisms. For braided commutative algebras the full subcategory of symmetric -bimodule objects is a braided closed monoidal category, from which we obtain an internal tensor product operation on internal homomorphisms. We describe how these structures deform under cochain twisting of the quasi-Hopf algebra, and apply the formalism to the example of deformation quantization of equivariant vector bundles over a smooth manifold. Our constructions set up the basic ingredients for the systematic development of differential geometry internal to the quasi-Hopf representation category, which will be tackled in the sequels to this paper, together with applications to models of noncommutative and nonassociative gravity such as those anticipated from non-geometric string theory. 相似文献
132.
133.
134.
《代数通讯》2013,41(7):3219-3249
Abstract Let R be a G-graded ring,M a G-graded Σ-quasiprojective R- module,and E = END R (M) its graded ring of endomorphisms. For any subgroup H of G,we prove that certain full subcategories of G/H-graded R-modules associated with M are equivalent to a quotient category of G/H-graded E-modules determined by the idempotent G-graded ideal of E consisting of endomorphisms which factor through a finitely generated submodule of M. Properties and applications of these equivalences are also examined. 相似文献
135.
This paper presents a new approach to the dimension theory of triangulated categories by considering invariants that arise in the pretriangulated setting. 相似文献
136.
This is the first paper in a series. We develop a general deformation theory of objects in homotopy and derived categories of DG categories. Namely, for a DG module E over a DG category we define four deformation functors Defh(E), coDefh(E), Def(E), coDef(E). The first two functors describe the deformations (and co-deformations) of E in the homotopy category, and the last two - in the derived category. We study their properties and relations. These functors are defined on the category of artinian (not necessarily commutative) DG algebras. 相似文献
137.
Marco Grandis 《Applied Categorical Structures》2006,14(3):191-214
We have introduced, in a previous paper, the fundamental lax 2-category of a ‘directed space’ . Here we show that, when
has a
-topology, this structure can be embedded into a larger one, with the same objects (the points of ), the same arrows (the directed paths) and the same cells (based on directed homotopies of paths), but a larger system of comparison cells. The new comparison cells are absolute, in the sense that they only depend on the arrows themselves rather than on their syntactic expression, as in the usual settings of lax or weak structures. It follows that, in the original structure, all the diagrams of comparison cells commute, even if not constructed in a natural way and even if the composed cells need not stay within the old system.Work supported by MIUR Research Projects. 相似文献
138.
Let C be a self-dual spherical fusion categories of rank 4 with non-trivial grading. We complete the classification of Grothendieck ring K(C) of C; that is, we prove that K(C)≌Fib■Z[Z_2],where Fib is the Fibonacci fusion ring and Z[Z_2] is the group ring on Z_2. In particular, if C is braided,then it is equivalent to Fib Ve■cω_(Z_2) as fusion categories, where Fib is a Fibonacci category and VecωZ_2 is a rank 2 pointed fusion category. 相似文献
139.
毛泽东诗词巨大而深刻的文化内涵和美学意蕴将愈来愈被国外读者所接受和喜爱。在对其进行翻译时,要充分考虑其语言图式、内容图式、文体图式和文化图式的正确传译,以使其精髓能够得到较好的传递,对我国文化传播产生积极的影响。 相似文献
140.