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.
Une loi distributive est une façon de composer deux structures algébriques, disons et , en une structure algébrique plus complexe . Le but de ce travail est de comprendre les lois distributives en termes d’opérades. Le résultat central dit que si les opérades correspondant à et sont de Koszul, alors l’opérade correspondant à est aussi de Koszul. On donne une application à la cohomologie des espaces de configurations.
@article{AIF_1996__46_2_307_0, author = {Markl, Martin}, title = {Distributive laws and {Koszulness}}, journal = {Annales de l'Institut Fourier}, pages = {307--323}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {46}, number = {2}, year = {1996}, doi = {10.5802/aif.1516}, mrnumber = {97i:18008}, zbl = {0853.18005}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1516/} }
TY - JOUR AU - Markl, Martin TI - Distributive laws and Koszulness JO - Annales de l'Institut Fourier PY - 1996 SP - 307 EP - 323 VL - 46 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1516/ DO - 10.5802/aif.1516 LA - en ID - AIF_1996__46_2_307_0 ER -
Markl, Martin. Distributive laws and Koszulness. Annales de l'Institut Fourier, Volume 46 (1996) no. 2, pp. 307-323. doi : 10.5802/aif.1516. http://archive.numdam.org/articles/10.5802/aif.1516/
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