Distributive laws and Koszulness

Martin Markl

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 2, page 307-323
  • ISSN: 0373-0956

Abstract

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Distributive law is a way to compose two algebraic structures, say and , into a more complex algebraic structure . 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 and are Koszul, then the operad corresponding to is Koszul as well. An application to the cohomology of configuration spaces is given.

How to cite

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Markl, Martin. "Distributive laws and Koszulness." Annales de l'institut Fourier 46.2 (1996): 307-323. <http://eudml.org/doc/75180>.

@article{Markl1996,
abstract = {Distributive law is a way to compose two algebraic structures, say $\{\cal U\}$ and $\{\cal V\}$, into a more complex algebraic structure $\{\cal W\}$. 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 $\{\cal U\}$ and $\{\cal V\}$ are Koszul, then the operad corresponding to $\{\cal W\}$ is Koszul as well. An application to the cohomology of configuration spaces is given.},
author = {Markl, Martin},
journal = {Annales de l'institut Fourier},
keywords = {distributive law; operad; koszulness; configuration spaces},
language = {eng},
number = {2},
pages = {307-323},
publisher = {Association des Annales de l'Institut Fourier},
title = {Distributive laws and Koszulness},
url = {http://eudml.org/doc/75180},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Markl, Martin
TI - Distributive laws and Koszulness
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 2
SP - 307
EP - 323
AB - Distributive law is a way to compose two algebraic structures, say ${\cal U}$ and ${\cal V}$, into a more complex algebraic structure ${\cal W}$. 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 ${\cal U}$ and ${\cal V}$ are Koszul, then the operad corresponding to ${\cal W}$ is Koszul as well. An application to the cohomology of configuration spaces is given.
LA - eng
KW - distributive law; operad; koszulness; configuration spaces
UR - http://eudml.org/doc/75180
ER -

References

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  1. [1] J. BECK, Distributive laws, Lecture Notes in Mathematics, 80 (1969), 119-140. Zbl0186.02902MR39 #2842
  2. [2] T.F. FOX and M. MARKL, Distributive laws, bialgebras, and cohomology, Contemporary Mathematics, to appear. Zbl0866.18008
  3. [3] W. FULTON and R. MACPHERSON, A compactification of configuration spaces, Annals of Mathematics, 139 (1994), 183-225. Zbl0820.14037MR95j:14002
  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. Zbl0676.16022MR90c:16016
  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. Zbl0855.18006MR96a:18004
  7. [7] M. MARKL, Models for operads, Communications in Algebra, 24(4) (1996), 1471-1500. Zbl0848.18003MR96m:18012
  8. [8] J.P. MAY, The Geometry of Iterated Loop Spaces, volume 271 of Lecture Notes in Mathematics, Springer-Verlag, 1972. Zbl0244.55009MR54 #8623b

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