Rational homotopy of Leibniz algebras

被引：25

作者：

Livernet, M

机构：

[1] Univ Strasbourg 1, Inst Rech Math Avancee, F-67084 Strasbourg, France

[2] CNRS, F-67084 Strasbourg, France

来源：

MANUSCRIPTA MATHEMATICA | 1998年 / 96卷 / 03期

关键词：

Mathematics Subject Classification (1991):55P62, 17A30, 18Gxx;

D O I：

10.1007/s002290050069

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a non-commutative rational homotopy theory by replacing the pail: (Lie algebras, commutative algebras) by the pair (Leibniz algebras, Leibniz-dual algebras). Both pairs are Koszul dual in the sense of operads (Ginzburg-Kapranov). We prove the existence of minimal models and the Hurewicz theorem in this framework. We define Leibniz spheres and prove that their homotopy is periodic.

引用

页码：295 / 315

页数：21

共 18 条

[1]

BALAVOINE D, 1997, THESIS U MONTPELLIER

[2] MINIMAL MODELS IN HOMOTOPY THEORY [J].