3,008 research outputs found
(Contravariant) Koszul duality for DG algebras
A DG algebras over a field with connected and
has a unique up to isomorphism DG module with . It is proved
that if is degreewise finite, then RHom_A(?,K): D^{df}_{+}(A)^{op}
\equiv D_{df}^{+}}(RHom_A(K,K)) is an exact equivalence of derived categories
of DG modules with degreewise finite-dimensional homology. It induces an
equivalences of and the category of perfect DG
-modules, and vice-versa. Corresponding statements are proved also
when is simply connected and .Comment: 33 page
Andre-Quillen cohomology of algebras over an operad
We study the Andre-Quillen cohomology with coefficients of an algebra over an
operad. Using resolutions of algebras coming from Koszul duality theory, we
make this cohomology theory explicit and we give a Lie theoretic
interpretation. For which operads is the associated Andre-Quillen cohomology
equal to an Ext-functor ? We give several criterion, based on the cotangent
complex, to characterize this property. We apply it to homotopy algebras, which
gives a new homotopy stable property for algebras over cofibrant operads.Comment: Corrections in Sections 5 and 6, to appear in Advances in Mathematic
D-structures and derived Koszul duality for unital operad algebras
Generalizing a concept of Lipshitz, Ozsv\'ath and Thurs-ton from Bordered
Floer homology, we define -structures on algebras of unital operads, which
can also be interpreted as a generalization of a seemingly unrelated concept of
Getzler and Jones. This construction gives rise to an equivalence of derived
categories, which can be thought of as a unital version of Koszul duality using
non-unital Quillen homology. We also discuss a multi-sorted version of the
construction, which provides a framework for unifying the known algebraic
contexts of Koszul duality.Comment: Accepted for Publication in J. Pure Appl. Al
On the logarithmic comparison theorem for integrable logarithmic connections
Let be a complex analytic manifold, a free divisor with
jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor),
the corresponding open inclusion, an integrable
logarithmic connection with respect to and the local system of the
horizontal sections of on . In this paper we prove that the canonical
morphisms between the logarithmic de Rham complex of and
(resp. the logarithmic de Rham complex of and ) are isomorphisms
in the derived category of sheaves of complex vector spaces for
(locally on )Comment: Terminology has changed: "linear jacobian type" instead of
"commutative differential type"); no Koszul hypothesis is needed in theorem
(2.1.1); minor changes. To appear in Proc. London Math. So
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