Koszul duality for operads

previous :: next

Koszul duality for operads

Victor Ginzburg and Mikhail Kapranov

Source: Duke Math. J. Volume 76, Number 1 (1994), 203-272.

First Page: Show

Related Works:

See also: V. Ginzburg, M. Kapranov. Erratum to “Koszul duality for operads,” vol. 76 (1994) pp. 203–272. Duke Math. J. Vol. 80, No. 1 (1995), pp. 293–293.

Project Euclid: euclid.dmj/1077245862

Primary Subjects: 18D10

Secondary Subjects: 14H10, 16S99, 18G50, 55P47

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077286744
Mathematical Reviews number (MathSciNet): MR1301191
Zentralblatt MATH identifier: 0855.18006
Digital Object Identifier: doi:10.1215/S0012-7094-94-07608-4

back to Table of Contents

References

[1] J. F. Adams, Infinite loop spaces, Annals of Mathematics Studies, vol. 90, Princeton University Press, Princeton, N.J., 1978.

Mathematical Reviews (MathSciNet): MR80d:55001

Zentralblatt MATH: 0398.55008

[2] V. I. Arnold, On the representation of continuous functions of three variables by superpositions of continuous functions of two variables, Mat. Sb. (N.S.) 48 (90) (1959), 3–74.

Mathematical Reviews (MathSciNet): MR22:12191

Zentralblatt MATH: 0090.27102

[3] V. I. Arnold, Topological invariants of algebraic functions II, Funct. Anal. Appl. 4 (1970), 91–98.

Zentralblatt MATH: 0239.14012

Mathematical Reviews (MathSciNet): MR276244

[4] H. Bass, E. H. Connell, and D. Wright, The Jacobian conjecture: reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 2, 287–330.

Mathematical Reviews (MathSciNet): MR83k:14028

Zentralblatt MATH: 0539.13012

Digital Object Identifier: doi:10.1090/S0273-0979-1982-15032-7

Project Euclid: euclid.bams/1183549636

[5] A. A. Beilinson, Coherent sheaves on $P^n$ and problems in linear algebra, Funct. Anal. Appl. 12 (1978), 214–216.

Mathematical Reviews (MathSciNet): MR509388

[6] I. N. Bernstein, I. M. Gelfand, and S. I. Gelfand, Algebraic vector bundles on $P^n$ and problems of linear algebra, Funct. Anal. Appl. 12 (1978), 212–214.

[7] A. A. Beilinson, V. A. Ginsburg, and V. V. Schechtman, Koszul duality, J. Geom. Phys. 5 (1988), no. 3, 317–350.

Mathematical Reviews (MathSciNet): MR91c:18011

Zentralblatt MATH: 0695.14009

Digital Object Identifier: doi:10.1016/0393-0440(88)90028-9

[8] A. Beilinson, V. Ginzburg, and W. Soergel, Koszul duality patterns in representation theory, to appear in J. Amer. Math. Soc.

Mathematical Reviews (MathSciNet): MR1322847

Zentralblatt MATH: 0864.17006

Digital Object Identifier: doi:10.1090/S0894-0347-96-00192-0

JSTOR: links.jstor.org

[9] A. Beilinson and V. Ginzburg, Infinitesimal structure of moduli spaces of $G$-bundles, Internat. Math. Res. Notices (1992), no. 4, 63–74.

Mathematical Reviews (MathSciNet): MR93g:14036

Zentralblatt MATH: 0763.32011

Digital Object Identifier: doi:10.1155/S1073792892000072

[10] A. Beilinson and V. Ginzburg, Resolution of diagonals homotopy algebra and moduli spaces, preprint.

[11] J. M. Boardman and R. M. Vogt, Homotopy invariant algebraic structures on topological spaces, Lecture Notes in Mathematics, vol. 347, Springer-Verlag, Berlin, 1973.

Mathematical Reviews (MathSciNet): MR54:8623a

Zentralblatt MATH: 0285.55012

[12] F. R. Cohen, The homology of $C_(n+1)$-spaces, Homology of Iterated Loop Spaces, Lecture Notes in Math., vol. 533, Springer-Verlag, Berlin, 1976, pp. 207–351.

Zentralblatt MATH: 0334.55009

[13] P. Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. (1971), no. 40, 5–57.

Mathematical Reviews (MathSciNet): MR58:16653a

Zentralblatt MATH: 0219.14007

Digital Object Identifier: doi:10.1007/BF02684692

[14] P. Deligne, Resumé des premiérs exposés de A. Grothendieck, Groupes de Monodromie en Géométrie Algébrique, Lecture Notes in Math., vol. 288, Springer-Verlag, Berlin, 1972, pp. 1–24.

Zentralblatt MATH: 0267.14003

[15] P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), no. 1, 103–161.

Mathematical Reviews (MathSciNet): MR52:14076

Zentralblatt MATH: 0336.20029

Digital Object Identifier: doi:10.2307/1971021

JSTOR: links.jstor.org

[16] P. Deligne and G. Lusztig, Duality for representations of a reductive group over a finite field, J. Algebra 74 (1982), no. 1, 284–291.

Mathematical Reviews (MathSciNet): MR83e:20041

Zentralblatt MATH: 0482.20027

Digital Object Identifier: doi:10.1016/0021-8693(82)90023-0

[17] P. Deligne and G. Lusztig, Duality for representations of a reductive group over a finite field. II, J. Algebra 81 (1983), no. 2, 540–545.

Mathematical Reviews (MathSciNet): MR85b:20058

Zentralblatt MATH: 0535.20020

Digital Object Identifier: doi:10.1016/0021-8693(83)90202-8

[18] V. G. Drinfeld, letter to V. V. Schechtman, unpublished, Septembre, 1988.

Mathematical Reviews (MathSciNet): MR869575

[19] H. Esnault, V. Schechtman, and E. Viehweg, Cohomology of local systems on the complement of hyperplanes, Invent. Math. 109 (1992), no. 3, 557–561.

Mathematical Reviews (MathSciNet): MR93g:32051

Zentralblatt MATH: 0788.32005

Digital Object Identifier: doi:10.1007/BF01232040

[20] Z. Fiedorowicz, The symmetric bar-construction, preprint, 1991.

[21] W. Fulton and R. MacPherson, A compactification of configuration spaces, Ann. of Math. (2) 139 (1994), no. 1, 183–225.

Mathematical Reviews (MathSciNet): MR95j:14002

Zentralblatt MATH: 0820.14037

Digital Object Identifier: doi:10.2307/2946631

[22] E. Getzler, Batalin-Vilkovisky algebras and two-dimensional topological field theories, Comm. Math. Phys. 159 (1994), no. 2, 265–285.

Mathematical Reviews (MathSciNet): MR95h:81099

Zentralblatt MATH: 0807.17026

Digital Object Identifier: doi:10.1007/BF02102639

Project Euclid: euclid.cmp/1104254599

[23] E. Getzler and J. D. S. Jones, Operads, homotopy algebra and iterated integrals for double loop spaces, preprint, 1994.

[24] R. Godement, Topologie algébrique et théorie des faisceaux, Hermann, Paris, 1973.

Mathematical Reviews (MathSciNet): MR49:9831

Zentralblatt MATH: 0275.55010

[25] I. J. Good, Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes, Proc. Cambridge Philos. Soc. 56 (1960), 367–380.

Mathematical Reviews (MathSciNet): MR23:A352

Zentralblatt MATH: 0135.18802

Digital Object Identifier: doi:10.1017/S0305004100034666

[26] M. Goresky and R. MacPherson, Stratified Morse theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 14, Springer-Verlag, Berlin, 1988.

Mathematical Reviews (MathSciNet): MR90d:57039

[27] V. A. Hinich and V. V. Schectman, On homotopy limit of homotopy algebras, $K$-theory, arithmetic and geometry (Moscow, 1984–1986), Lecture Notes in Math., vol. 1289, Springer, Berlin, 1987, pp. 240–264.

Mathematical Reviews (MathSciNet): MR89d:55052

Zentralblatt MATH: 0631.55011

Digital Object Identifier: doi:10.1007/BFb0078370

[28] V. Hinich and V. Schechtman, Homotopy Lie algebras, I. M. Gelfand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 1–28.

Mathematical Reviews (MathSciNet): MR95c:18009

Zentralblatt MATH: 0823.18004

[29] S. A. Joni, Lagrange inversion in higher dimensions and umbral operators, Linear and Multilinear Algebra 6 (1978/79), no. 2, 111–122.

Mathematical Reviews (MathSciNet): MR58:10485

Zentralblatt MATH: 0395.05005

Digital Object Identifier: doi:10.1080/03081087808817229

[30] M. M. Kapranov, On the derived categories and the $K$-functor of coherent sheaves on intersections of quadrics, Math. USSR-Izv. 32 (1989), 191–204.

Zentralblatt MATH: 0679.14005

Mathematical Reviews (MathSciNet): MR936529

[31] M. M. Kapranov, Veronese curves and Grothendieck-Knudsen moduli space $\overline M\sb 0,n$, J. Algebraic Geom. 2 (1993), no. 2, 239–262.

Mathematical Reviews (MathSciNet): MR94a:14024

Zentralblatt MATH: 0790.14020

[32] M. M. Kapranov, Chow quotients of Grassmannians. I, I. M. Gelfand Seminar, Adv. Soviet Math., vol. 16, Amer. Math. Soc., Providence, RI, 1993, pp. 29–110.

Mathematical Reviews (MathSciNet): MR95g:14053

Zentralblatt MATH: 0811.14043

[33] M. M. Kapranov, On the derived categories of coherent sheaves on some homogeneous spaces, Invent. Math. 92 (1988), no. 3, 479–508.

Mathematical Reviews (MathSciNet): MR89g:18018

Zentralblatt MATH: 0651.18008

Digital Object Identifier: doi:10.1007/BF01393744

[34] M. Kashiwara and P. Schapira, Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 292, Springer-Verlag, Berlin, 1990.

Mathematical Reviews (MathSciNet): MR92a:58132

Zentralblatt MATH: 0709.18001

[35] A. A. Klyachko, Lie elements in the tensor algebra, Siberian Math. J. 15 (1974), 914–920.

[36] F. F. Knudsen, The projectivity of the moduli space of stable curves. II. The stacks $M\sbg,n$, Math. Scand. 52 (1983), no. 2, 161–199.

Mathematical Reviews (MathSciNet): MR85d:14038a

Zentralblatt MATH: 0544.14020

[37] A. N. Kolmogorov, On the representation of continuous functions of several variables by superpositions of continuous functions of a smaller number of variables, Dokl. Akad. Nauk SSSR (N.S.) 108 (1956), 179–182, (in Russian); reprinted in Selected Works of A. N. Kolmogorov, Vol. I, ed. by V. Tikhomirov, Kluwer, Dordrecht, 1991, 378–382.

Mathematical Reviews (MathSciNet): MR18,197b

Zentralblatt MATH: 0128.27803

[38] M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function, Comm. Math. Phys. 147 (1992), no. 1, 1–23.

Mathematical Reviews (MathSciNet): MR93e:32027

Zentralblatt MATH: 0756.35081

Digital Object Identifier: doi:10.1007/BF02099526

Project Euclid: euclid.cmp/1104250524

[39] M. Kontsevich, Formal (non)commutative symplectic geometry, The Gelfand Mathematical Seminars, 1990–1992 eds. L. Crowin, I. Gelfand, and J. Lepowsky, Birkhäuser Boston, Boston, MA, 1993, pp. 173–187.

Mathematical Reviews (MathSciNet): MR94i:58212

Zentralblatt MATH: 0821.58018

[40] M. Kontsevich, Graphs, homotopy Lie and low-dimensional topology, preprint, 1992.

[41] I. Kriz and J. P. May, Oprads, algebras and modules I, preprint, 1993.

[42] I. Kriz and J. P. May, Differential graded algebras up to homotopy and their derived categories, preprint, 1992.

[43] M. Lazard, Lois de groupes et analyseurs, Ann. Sci. Ecole Norm. Sup. (3) 72 (1955), 299–400.

Mathematical Reviews (MathSciNet): MR17,1053c

Zentralblatt MATH: 0068.02702

[44] B. Lian and G. Zuckerman, New perspectives on the BRST-Algebraic structures of string theory, preprint, 1992.

Mathematical Reviews (MathSciNet): MR1224094

Zentralblatt MATH: 0780.17029

Digital Object Identifier: doi:10.1007/BF02102111

Project Euclid: euclid.cmp/1104253081

[45] J.-L. Loday, Cyclic homology, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 301, Springer-Verlag, Berlin, 1992.

Mathematical Reviews (MathSciNet): MR94a:19004

Zentralblatt MATH: 0780.18009

[46] C. Löfwall, On the subalgebra generated by the one-dimensional elements in the Yoneda Ext-algebra, Algebra, algebraic topology and their interactions (Stockholm, 1983), Lecture Notes in Math., vol. 1183, Springer, Berlin, 1986, pp. 291–338.

Mathematical Reviews (MathSciNet): MR88f:16030

Zentralblatt MATH: 0595.16020

[47] G. Lusztig, The discrete Series of $GL\sbn$ over a Finite Field, Annals of Mathematics Studies, vol. 81, Princeton University Press, Princeton, N.J., 1974.

Mathematical Reviews (MathSciNet): MR52:3303

Zentralblatt MATH: 0293.20038

[48] J. H. McKay, J. Towber, S. S.-S. Wang, and D. Wright, Reversion of a system of power series with application to combinatorics, preprint, 1992.

[49]¹ Saunders Mac Lane, Natural associativity and commutativity, Rice Univ. Studies 49 (1963), no. 4, 28–46.

Mathematical Reviews (MathSciNet): MR30:1160

Zentralblatt MATH: 0244.18008

[49]² Saunders Mac Lane, Selected papers, Springer-Verlag, New York, 1979.

Mathematical Reviews (MathSciNet): MR80k:01064

Zentralblatt MATH: 0459.01024

[50] I. G. Macdonald, Symmetric functions and Hall polynomials, The Clarendon Press Oxford University Press, New York, 1979.

Mathematical Reviews (MathSciNet): MR84g:05003

Zentralblatt MATH: 0487.20007

[51] Y. I. Manin, Some remarks on Koszul algebras and quantum groups, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 4, 191–205.

Mathematical Reviews (MathSciNet): MR89e:16022

Zentralblatt MATH: 0625.58040

[52] J. P. May, The Geometry of Iterated Loop Spaces, Lectures Notes in Mathematics, vol. 271, Springer-Verlag, Berlin, 1972.

Mathematical Reviews (MathSciNet): MR54:8623b

Zentralblatt MATH: 0244.55009

[53] J. C. Moore, Differential homological algebra, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 1, Gauthier-Villars, Paris, 1971, pp. 335–339.

Mathematical Reviews (MathSciNet): MR55:9128

Zentralblatt MATH: 0337.18009

[54] R. C. Penner, The decorated Teichmüller space of punctured surfaces, Comm. Math. Phys. 113 (1987), no. 2, 299–339.

Mathematical Reviews (MathSciNet): MR89h:32044

Zentralblatt MATH: 0642.32012

Digital Object Identifier: doi:10.1007/BF01223515

Project Euclid: euclid.cmp/1104160216

[55] S. B. Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970), 39–60.

Mathematical Reviews (MathSciNet): MR42:346

Zentralblatt MATH: 0261.18016

Digital Object Identifier: doi:10.2307/1995637

JSTOR: links.jstor.org

[56] D. Quillen, Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205–295.

Mathematical Reviews (MathSciNet): MR41:2678

Zentralblatt MATH: 0191.53702

Digital Object Identifier: doi:10.2307/1970725

JSTOR: links.jstor.org

[57] D. Quillen, On the (co-) homology of commutative rings, Applications of Categorical Algebra (Proc. Sympos. Pure Math., Vol. XVII, New York, 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 65–87.

Mathematical Reviews (MathSciNet): MR41:1722

Zentralblatt MATH: 0234.18010

[58] V. V. Schechtman and A. N. Varchenko, Arrangements of hyperplanes and Lie algebra homology, Invent. Math. 106 (1991), no. 1, 139–194.

Mathematical Reviews (MathSciNet): MR93b:17067

Zentralblatt MATH: 0754.17024

Digital Object Identifier: doi:10.1007/BF01243909

[59] M. Schlessinger and J. Stasheff, The Lie algebra structure of tangent cohomology and deformation theory, J. Pure Appl. Algebra 38 (1985), no. 2-3, 313–322.

Mathematical Reviews (MathSciNet): MR87e:13019

Zentralblatt MATH: 0576.17008

Digital Object Identifier: doi:10.1016/0022-4049(85)90019-2

[60] J. D. Stasheff, Homotopy associativity of $H$-spaces. I, II, Trans. Amer. Math. Soc. 108 (1963), 275-292; ibid. 108 (1963), 293–312.

Mathematical Reviews (MathSciNet): MR28:1623

Zentralblatt MATH: 0114.39402

Digital Object Identifier: doi:10.2307/1993609

[61] J. J. Sylvester, On the change of systems of independent variables, Quart. J. Math. 1 (1857), 42–56.

[62] D. Wright, The tree formulas for reversion of power series, J. Pure Appl. Algebra 57 (1989), no. 2, 191–211.

Mathematical Reviews (MathSciNet): MR90d:13008

Zentralblatt MATH: 0672.13010

Digital Object Identifier: doi:10.1016/0022-4049(89)90116-3

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?