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Homological Algebra of Mirror Symmetry
 in Proceedings of the International Congress of Mathematicians
, 1994
"... Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual Ca ..."
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Cited by 529 (3 self)
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Mirror Symmetry was discovered several years ago in string theory as a duality between families of 3dimensional CalabiYau manifolds (more precisely, complex algebraic manifolds possessing holomorphic volume elements without zeroes). The name comes from the symmetry among Hodge numbers. For dual
Homological algebra of homotopy algebras
 Communications in Algebra
"... Abstract. Theorem 6.1.1 of [H] on the existence of a model structure on the category of operads is not valid in the generality claimed. We present a counterexample (due to B. Fresse) and a corrected version of the theorem. 1. In [H] we claimed the following result which turned out to be partly wron ..."
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Cited by 140 (8 self)
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Abstract. Theorem 6.1.1 of [H] on the existence of a model structure on the category of operads is not valid in the generality claimed. We present a counterexample (due to B. Fresse) and a corrected version of the theorem. 1. In [H] we claimed the following result which turned out to be partly wrong (see the counterexample below).
HISTORY OF HOMOLOGICAL ALGEBRA
"... Homological algebra had its origins in the 19th century, via the work of Riemann ..."
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Cited by 3 (0 self)
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Homological algebra had its origins in the 19th century, via the work of Riemann
On the qanalog of homological algebra
, 1991
"... Homological algebra can be seen as the study of the equation d 2 = 0 (see the epigraph to [1]). It is natural to ask why d 2 and not, say, d 3. Following this mood, we give the ..."
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Cited by 39 (0 self)
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Homological algebra can be seen as the study of the equation d 2 = 0 (see the epigraph to [1]). It is natural to ask why d 2 and not, say, d 3. Following this mood, we give the
Constructive Homological Algebra and Applications
"... Standard homological algebra is not constructive, and this is frequently the source of serious problems when algorithms are looked for. In particular the usual exact and spectral sequences of homological algebra frequently are in general not sufficient to obtain some unknown homology or homotopy gr ..."
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Standard homological algebra is not constructive, and this is frequently the source of serious problems when algorithms are looked for. In particular the usual exact and spectral sequences of homological algebra frequently are in general not sufficient to obtain some unknown homology or homotopy
Homological algebra of semimodules and semicontramodules
, 2007
"... Abstract. We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define doublesided derived functors SemiTor and SemiExt of ..."
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Cited by 15 (7 self)
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Abstract. We develop the basic constructions of homological algebra in the (appropriately defined) unbounded derived categories of modules over algebras over coalgebras over noncommutative rings (which we call semialgebras over corings). We define doublesided derived functors SemiTor and Semi
HOMOLOGICAL ALGEBRA FOR SCHWARTZ ALGEBRAS
"... Abstract. Let G be a reductive group over a nonArchimedean local field. For two tempered smooth representations, it makes no difference for the Extgroups whether we work in the category of tempered smooth representations of G or of all smooth representations of G. Similar results hold for certain ..."
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Abstract. Let G be a reductive group over a nonArchimedean local field. For two tempered smooth representations, it makes no difference for the Extgroups whether we work in the category of tempered smooth representations of G or of all smooth representations of G. Similar results hold for certain discrete groups. We explain the basic ideas from functional analysis and geometric group theory that are needed to state this result correctly and prove it. 1.
INTERSECTION HOMOLOGICAL ALGEBRA
"... Abstract. We investigate the abelian category which is the target of intersection homology. Recall that, given a stratified space X, we get intersection homology groups IpHnX depending on the choice of an nperversity p. The nperversities form a lattice, and we can think of IHnX as a functor from t ..."
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Cited by 3 (2 self)
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Abstract. We investigate the abelian category which is the target of intersection homology. Recall that, given a stratified space X, we get intersection homology groups IpHnX depending on the choice of an nperversity p. The nperversities form a lattice, and we can think of IHnX as a functor from
Homological Algebra and Divergent Series
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2009
"... We study some features of infinite resolutions of Koszul algebras motivated by the developments in the string theory initiated by Berkovits. ..."
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We study some features of infinite resolutions of Koszul algebras motivated by the developments in the string theory initiated by Berkovits.
Results 1  10
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40,484