Open-Closed Homotopy Algebras and Strong Homotopy Leibniz Pairs Through Koszul Operad Theory

被引：0
作者：
Eduardo Hoefel
Muriel Livernet
机构：
[1] Universidade Federal do Paraná,Departamento de Matemática
[2] Université Paris 13,undefined
[3] CNRS,undefined
[4] UMR 7539 LAGA,undefined
来源：
Letters in Mathematical Physics | 2012年 / 101卷
关键词：
18G55; 18D50; Koszul Operads; homotopy algebras; deformation theory;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Open-closed homotopy algebras (OCHA) and strong homotopy Leibniz pairs (SHLP) were introduced by Kajiura and Stasheff in 2004. In an appendix to their paper, Markl observed that an SHLP is equivalent to an algebra over the minimal model of a certain operad, without showing that the operad is Koszul. In the present paper, we show that both OCHA and SHLP are algebras over the minimal model of the zeroth homology of two versions of the Swiss-cheese operad and prove that these two operads are Koszul. As an application, we show that the OCHA operad is non-formal as a 2-colored operad but is formal as an algebra in the category of 2-collections.
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页码：195 / 222
页数：27
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共 20 条
  • [1] Dolgushev V.(2011)Formality theorem for Hochschild cochains via transfer Lett. Math. Phys. 97 109-149
  • [2] Flato M.(1995)Cohomology and deformation of Leibniz pairs Lett. Math. Phys. 34 77-90
  • [3] Gerstenhaber M.(1963)The cohomology structure of an associative ring Ann. Maths 78 267-288
  • [4] Voronov A.A.(1990)-algebras and the cyclic bar complex Ill. J. Math. 34 256-283
  • [5] Gerstenhaber M.(1994)Koszul duality for operads Duke Math. J. 76 203-272
  • [6] Getzler E.(2009)OCHA and the Swiss-cheese operad J. Hom. Relat. Struct. 4 123-151
  • [7] Jones J.D.S.(2012)On the coalgebra description of OCHA J. Pure Appl. Algebra 216 734-741
  • [8] Ginzburg V.(2006)Homotopy algebras inspired by classical open-closed string field theory Commun. Math. Phys. 263 553-581
  • [9] Kapranov M.(2006)Open-closed homotopy algebra in mathematical physics J. Math. Phys. 47 28-72
  • [10] Hoefel E.(1999)Operads and motives in deformation quantization Lett. Math. Phys. 48 35-216
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