L∞ structures on mapping cones

被引：51
作者：
Fiorenza, Domenico [1 ]
Manetti, Marco [1 ]
机构：
[1] Univ Roma La Sapienza, Dipartimento Matemat Guido Castelnuovo, I-00185 Rome, Italy
来源：
ALGEBRA & NUMBER THEORY | 2007年 / 1卷 / 03期
关键词：
differential graded Lie algebra; symmetric coalgebra; L-infinity-algebra; functor of Artin ring; DEFORMATIONS; ALGEBRAS; FUNCTORS;
D O I：
10.2140/ant.2007.1.301
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the mapping cone of a morphism of differential graded Lie algebras, chi : L -> M, can be canonically endowed with an L-infinity-algebra structure which at the same time lifts the Lie algebra structure on L and the usual differential on the mapping cone. Moreover, this structure is unique up to isomorphisms of L-infinity-algebras.
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页码：301 / 330
页数：30
相关论文
共 35 条
[1]  
BERING K, 2006, HEPTH0603116
[2]  
CHEN G, 2006, MATHAT0610912
[3]   INTEGRATION OF PATHS, GEOMETRIC INVARIANTS AND A GENERALIZED BAKER-HAUSDORFF FORMULA [J].
CHEN, KT .
ANNALS OF MATHEMATICS, 1957, 65 (01) :163-178
[4]   Geometry of formal Kuranishi theory [J].
Clemens, H .
ADVANCES IN MATHEMATICS, 2005, 198 (01) :311-365
[5]  
Dupont J.L., 1978, Lecture Notes in Mathematics, V640
[6]   SIMPLICIAL DE RHAM COHOMOLOGY AND CHARACTERISTIC CLASSES OF FLAT BUNDLES [J].
DUPONT, JL .
TOPOLOGY, 1976, 15 (03) :233-245
[7]   Obstruction calculus for functors of Artin rings, I [J].
Fantechi, B ;
Manetti, M .
JOURNAL OF ALGEBRA, 1998, 202 (02) :541-576
[8]  
FIORENZA D, 2006, MATH0605297
[9]  
Fukaya K, 2003, STUD HI ENER PHY COS, P121
[10]  
GETZLER E, 2004, ANN MATH IN PRESS
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