24,048 research outputs found

    A generic algebra associated to certain Hecke algebras

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    We initiate the systematic study of endomorphism algebras of permutation modules and show they are obtainable by a descent from a certain "generic" Hecke algebra, infinite-dimensional in general, coming from the universal enveloping algebra of gl_n (or sl_n). The endomorphism algebras and the generic algebras are cellular. We give several equivalent descriptions of these algebras, find a number of explicit bases, and describe indexing sets for their irreducible representations.Comment: 19 page

    Silted algebras

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    We study endomorphism algebras of 2-term silting complexes in derived categories of hereditary finite dimensional algebras, or more generally of Ext\mathop{\rm Ext}\nolimits-finite hereditary abelian categories. Module categories of such endomorphism algebras are known to occur as hearts of certain bounded tt-structures in such derived categories. We show that the algebras occurring are exactly the algebras of small homological dimension, which are algebras characterized by the property that each indecomposable module either has injective dimension at most one, or it has projective dimension at most one.Comment: Fix some typos, to appear in Adv. Mat

    Hodge structures of type (n,0,...,0,n)

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    This paper determines all the possible endomorphism algebras for polarizable Q-Hodge structures of type (n,0,...,0,n). This generalizes the classification of the possible endomorphism algebras of abelian varieties by Albert and Shimura. As with abelian varieties, the most interesting feature of the classification is that in certain cases, every Hodge structure on which a given algebra acts must have extra endomorphisms.Comment: 19 page

    On derived equivalences of lines, rectangles and triangles

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    We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are "componentwise" tensor products, allowing us to obtain many derived equivalences that have not been observed by using previous techniques. Particular examples include algebras generalizing the ADE-chain related to singularity theory, incidence algebras of posets and certain Auslander algebras or more generally endomorphism algebras of initial preprojective modules over path algebras of quivers. Many of these algebras are fractionally Calabi-Yau and we explicitly compute their CY dimensions. Among the quivers of these algebras one can find shapes of lines, rectangles and triangles.Comment: v3: 21 pages. Slight revision, to appear in the Journal of the London Mathematical Society; v2: 20 pages. Minor changes, pictures and references adde

    Derived autoequivalences from periodic algebras

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    We present a construction of autoequivalences of derived categories of symmetric algebras based on projective modules with periodic endomorphism algebras. This construction generalises autoequivalences previously constructed by Rouquier-Zimmermann and is related to the autoequivalences of Seidel-Thomas and Huybrechts-Thomas. We show that compositions and inverses of these equivalences are controlled by the resolutions of our endomorphism algebra and that each autoequivalence can be obtained by certain compositions of derived equivalences between algebras which are in general not Morita equivalent.Comment: 34 pages; v2 is post referee report. The biggest changes from v1 are in Section 5.2. Final version has appeared in Proc. LM
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