Derived categories and tilting
WebMay 15, 2024 · Given small dg categories A and B and a B-A-bimodule T, we give necessary and sufficient conditions for the associated derived functors of Hom and the tensor product to be fully faithful. Special emphasis is put on the case when RHom $$_\\mathrm{A}$$ A (T,?) is fully faithful and preserves compact objects, in which case … WebMar 14, 2024 · SMCs were first studied by in the context of derived categories of symmetric algebras and they were also studied by under the name “cohomologically Schurian set of generators”. The name “SMC” was introduced by [ 29 , Definition 3.2] in general setting.
Derived categories and tilting
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WebWe review the basic definitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel’s theorem which … WebIn mathematics, specifically representation theory, tilting theory describes a way to relate the module categories of two algebras using so-called tilting modules and associated tilting functors.Here, the second algebra is the endomorphism algebra of a tilting module over the first algebra.. Tilting theory was motivated by the introduction of reflection …
WebDERIVED CATEGORIES AND TILTING BERNHARD KELLER Abstract. We review the basic definitions of derived categories and derived functors. We illustrate them on … WebNov 21, 2024 · A reduction approach to silting objects for derived categories of hereditary categories. Wei Dai, Changjian Fu. Let be a hereditary abelian category over a field with finite dimensional and spaces. It is proved that the bounded derived category has a silting object iff has a tilting object iff has a simple-minded collection with acyclic -quiver.
WebMay 1, 2024 · Silting and cosilting complexes in the derived category of a ring generalise tilting and cotilting modules. They give rise to subcategories of the derived category, … WebWe generalize tilting with respect to a tilting module of projective dimension at most one for an Artin algebra to tilting with respect to a torsion pair in an Abelian category. Our construction is motivated by the connection between tilting and derived categories. We develop a general theory for such tilting, and are led to a generalization of tilting …
WebMay 25, 2010 · Derived (and triangulated) categories were introduced by Verdier in his thesis (see [26, 79]) in order to simplify homological algebra. From this point of view the role of derived categories is purely technical.
WebNov 24, 1989 · Every projective-injective indecomposable module P for an algebra must be a direct summand of every tilting or cotilting module for that algebra by a remark of … canon tr8620 wireless connectionWebFeb 25, 2016 · The bike will have the latest iteration of Triumph's 1050cc engine. It also comes with three power modes (Road, Rain, and Sport) and cruise control. Full spec's and pricing will be announced at a later date.Triumph unveils two new limited edition American cruisers, 25 each model and the bikes will be numbered and carry a certificate of ... flagyl worksWebMay 25, 2010 · We review the basic definitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel's theorem which states that each tilting triple yields an equivalence between derived categories. flagyl wound gelWebA tilting complex T over A is an object in Kb(P(A)) which satisfies the following conditions: (I) for all i ≠ 0, the set HomDb(A)(T, T[i]) of homomorphisms in Db(A) vanishes, (II) the category add(T) (that is, the full subcategory of all direct sums of direct summands of T inside Kb(P(A))) generates Kb(P(A)) as a triangulated category. flagyl with amoxicillin for dental infectionsWeb2004. Abstract. We review the basic definitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel's theorem … canon track by order numberWebWe review the basic definitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel’s theorem which … flagyl y cistitisWebWe review the basic definitions of derived categories and derived functors. We illustrate them on simple but non trivial examples. Then we explain Happel's theorem which states … flagyl yeast infection vaginal