Almost D-split sequences and derived equivalences

نویسنده

  • Wei Hu
چکیده

In this paper, we introduce almost D-split sequences and establish an elementary but somewhat surprising connection between derived equivalences and Auslander-Reiten sequences via BB-tilting modules. In particular, we obtain derived equivalences from Auslander-Reiten sequences (or n-almost split sequences), and Auslander-Reiten triangles.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On iterated almost ν-stable derived equivalences

In a recent paper [5], we introduced a classes of derived equivalences called almost ν-stable derived equivalences. The most important property is that an almost ν-stable derived equivalence always induces a stable equivalence of Morita type, which generalizes a well-known result of Rickard: derived-equivalent self-injective algebras are stably equivalent of Morita type. In this paper, we shall...

متن کامل

ON THE USE OF KULSHAMMER TYPE INVARIANTS IN REPRESENTATION THEORY

Since 2005 a new powerful invariant of an algebra has emerged using the earlier work of Horvath, Hethelyi, Kulshammer and Murray. The authors studied Morita invariance of a sequence of ideals of the center of a nite dimensional algebra over a eld of nite characteristic. It was shown that the sequence of ideals is actually a derived invariant, and most recently a slightly modied version o...

متن کامل

On F -Almost Split Sequences

Let Λ be an Artinian algebra and F an additive subbifunctor of ExtΛ(−,−) having enough projectives and injectives. We prove that the dualizing subvarieties of mod Λ closed under F -extensions have F -almost split sequences. Let T be an F -cotilting module in mod Λ and S a cotilting module over Γ = End(T ). Then Hom(−, T ) induces a duality between F -almost split sequences in ⊥F T and almost sp...

متن کامل

Local Theory of Almost Split Sequences for Comodules

We show that almost split sequences in the category of comodules over a coalgebra Γ with finite-dimensional right-hand term are direct limits of almost split sequences over finite dimensional subcoalgebras. In previous work we showed that such almost split sequences exist if the right hand term has a quasifinitely copresented linear dual. Conversely, taking limits of almost split sequences over...

متن کامل

On Stable Equivalences of Morita Type for Finite Dimensional Algebras

In this paper, we assume that algebras are finite dimensional algebras with 1 over a fixed field k and modules over an algebra are finitely generated left unitary modules. Let A and B be two algebras (where k is a splitting field for A and B) with no semisimple summands. If two bimodules AMB and BNA induce a stable equivalence of Morita type between A and B, and if N⊗A− maps any simple A-module...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008