journal article
Jan 01, 1996
Distributive laws and Koszulness
Abstract
Distributive law is a way to compose two algebraic structures, say
𝒰
and
𝒱
, into a more complex algebraic structure
𝒲
. The aim of this paper is to understand distributive laws in terms of operads. The central result says that if the operads corresponding respectively to
𝒰
and
𝒱
are Koszul, then the operad corresponding to
𝒲
is Koszul as well. An application to the cohomology of configuration spaces is given.
𝒰
and
𝒱
, into a more complex algebraic structure
𝒲
. The aim of this paper is to understand distributive laws in terms of operads. The central result says that if the operads corresponding respectively to
𝒰
and
𝒱
are Koszul, then the operad corresponding to
𝒲
is Koszul as well. An application to the cohomology of configuration spaces is given.
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References
8
[1]
[1] J. Beck, Distributive laws, Lecture Notes in Mathematics, 80 (1969), 119-140.
[2]
[2] T.F. Fox and M. Markl, Distributive laws, bialgebras, and cohomology, Contemporary Mathematics, to appear.
[3]
[3] W. Fulton and R. Macpherson, A compactification of configuration spaces, Annals of Mathematics, 139 (1994), 183-225.
[4]
[4] M. Gerstenhaber and S.D. Schack, Algebraic cohomology and deformation theory. In Deformation Theory of Algebras and Structures and Applications, pages 11-264. Kluwer, Dordrecht, 1988.
[5]
[5] E. Getzler and J.D.S. Jones, Operads, homotopy algebra, and iterated integrals for double loop spaces, preprint, 1993.
[6]
[6] V. Ginzburg and M. Kapranov, Koszul duality for operads, Duke Math. Journal, 76(1) (1994), 203-272.
[7]
[7] M. Markl, Models for operads, Communications in Algebra, 24(4) (1996), 1471-1500.
[8]
[8] J.P. May, The Geometry of Iterated Loop Spaces, volume 271 of Lecture Notes in Mathematics, Springer-Verlag, 1972.
Metrics
54
Citations
8
References
Details
- Published
- Jan 01, 1996
- Vol/Issue
- 46(2)
- Pages
- 307-323
Authors
Cite This Article
Martin Markl (1996). Distributive laws and Koszulness. Annales de l'Institut Fourier, 46(2), 307-323. https://doi.org/10.5802/aif.1516
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