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The PfaffianGrassmannian derived equivalence
, 2006
"... We argue that there exists a derived equivalence between CalabiYau threefolds obtained by taking dual linear sections (of the appropriate codimension) of the Grassmannian G(2, 7) and the Pfaffian Pf(7). The existence of such an equivalence has been conjectured by physicists for almost ten years, as ..."
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We argue that there exists a derived equivalence between CalabiYau threefolds obtained by taking dual linear sections (of the appropriate codimension) of the Grassmannian G(2, 7) and the Pfaffian Pf(7). The existence of such an equivalence has been conjectured by physicists for almost ten years
Parsing And Derivational Equivalence
 In EACL 4
, 1989
"... It is a tacit assumption of much linguistic inquiry that all distinct derivations of a string should assign distinct meanings. But despite the tidiness of such derlvational uniqueness, there seems to be no a priori reason to assume that a gramma r must have this property. If a grammar exhibits deriv ..."
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Cited by 30 (5 self)
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derivational equivalence, whereby distinct derivations of a string assign the same meanings, naive exhaustive search for all derivations will be redundant, and quite possibly intractable. In this paper we show how notions of derivationreduction and normal form can be used to avoid unnecessary work while
ON DERIVED EQUIVALENCES FOR SELFINJECTIVE ALGEBRAS
"... Abstract. We show that if A is a representationfinite selfinjective artin algebra then every P • ∈ Kb(PA) with HomK(ModA)(P •, P •[i]) = 0 for i 6 = 0 and add(P •) = add(νP •) is a direct summand of a tilting complex, and that if A, B are derived equivalent representationfinite selfinjective a ..."
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Abstract. We show that if A is a representationfinite selfinjective artin algebra then every P • ∈ Kb(PA) with HomK(ModA)(P •, P •[i]) = 0 for i 6 = 0 and add(P •) = add(νP •) is a direct summand of a tilting complex, and that if A, B are derived equivalent representationfinite selfinjective
STANDARD DERIVED EQUIVALENCE FOR
"... Dedicated to Professor Idun Reiten on the occasion of her 60th birthday Abstract. We shall show that every stable equivalence (functor) between representationfinite selfinjective algebras not of type (D3m, s/3, 1) with m ¸ 2, 3 s lifts to a standard derived equivalence. This implies that all sta ..."
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Dedicated to Professor Idun Reiten on the occasion of her 60th birthday Abstract. We shall show that every stable equivalence (functor) between representationfinite selfinjective algebras not of type (D3m, s/3, 1) with m ¸ 2, 3 s lifts to a standard derived equivalence. This implies that all
Derived equivalence of orders
 PROCEEDINGS OF THE ICRA VII MEXICO. CAN MATH. SOC. CONFERENCE PROC 18
, 1996
"... Using the result of Roggenkamp and Scott [33] that the padic group ring of a pgroup determines its group bases we prove that for a p{group G, the derived equivalence class of the group ring over the padic integers determines the group basis up to isomorphism. We furthermore prove that two Green o ..."
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Using the result of Roggenkamp and Scott [33] that the padic group ring of a pgroup determines its group bases we prove that for a p{group G, the derived equivalence class of the group ring over the padic integers determines the group basis up to isomorphism. We furthermore prove that two Green
CLUSTER EQUIVALENCE AND GRADED DERIVED EQUIVALENCE
"... Abstract. In this paper we introduce a new approach for organizing algebras of global dimension at most 2. We introduce an invariant of these algebras called cluster equivalence, based on whether their generalized cluster categories are equivalent. We are particularly interested in the question how ..."
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observe that cluster tilting objects in generalized cluster categories are in natural bijection to cluster tilting subcategories of derived categories, and then prove a recognition theorem for the latter. Using this recognition theorem we give a precise criterion when two cluster equivalent algebras
KTheory and Derived Equivalences
, 2003
"... We show that if two rings have equivalent derived categories then they have the same algebraic Ktheory. Similar results are given for Gtheory, and for a large class of abelian categories. ..."
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Cited by 45 (7 self)
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We show that if two rings have equivalent derived categories then they have the same algebraic Ktheory. Similar results are given for Gtheory, and for a large class of abelian categories.
DERIVED EQUIVALENCES FOR ENDOMORPHISM RINGS
"... Abstract. We provide derived equivalences for endomorphism rings associated with a certain exact sequences. 1. Notation For a ring A, we denote by ModA the category of right Amodules, by modA the full subcategory of ModA consisting of finitely presented modules and by PA the full subcategory of ..."
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Abstract. We provide derived equivalences for endomorphism rings associated with a certain exact sequences. 1. Notation For a ring A, we denote by ModA the category of right Amodules, by modA the full subcategory of ModA consisting of finitely presented modules and by PA the full subcategory
Derived equivalences and Gorenstein algebras
 J. Pure Appl. Algebra
, 2007
"... In this note, we introduce the notion of Gorenstein algebras. Let R be a commutative Gorenstein ring and A a noetherian Ralgebra. We call A a Gorenstein Ralgebra if A has Gorenstein dimension zero as an Rmodule (see [2]), add(D(AA)) = PA, where D = HomR(−, R), and Ap is projective as an Rpmod ..."
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for some i ∈ Z. Unfortunately, the class of Gorenstein Ralgebras is not closed under derived equivalence in general (see Example 4.9). In Section 4, for a tilting complex P • over a Gorenstein Ralgebra A we show that B = EndK(ModA)(P •) is also a Gorenstein Ralgebra if and only if add(P •) = add
Results 1  10
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