Quantization of the Lie Bialgebra of String Topology

被引：7

作者：

Chen, Xiaojun ^{[1
]}

Eshmatov, Farkhod ^{[1
]}

Gan, Wee Liang ^{[2
]}

机构：

[1] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[2] Univ Calif Riverside, Dept Math, Riverside, CA 92521 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2011年 / 301卷 / 01期

关键词：

HOMOLOGY;

D O I：

10.1007/s00220-010-1139-z

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M. Using a Poincar, duality model for M, we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct a Hopf algebra which quantizes the Lie bialgebra.

引用

页码：37 / 53

页数：17

共 24 条

[1] Abbaspour H., 2008, ALGEBRAIC STRING BRA
[2] String bracket and flat connections
Abbaspour, Hossein
Zeinalian, Mahmoud
[J]. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2007, 7 : 197 - 231
[3] Andersen JE, 1998, MATH PROC CAMBRIDGE, V124, P451
[4] The Poisson structure on the moduli space of flat connections and chord diagrams
Andersen, JE
Mattes, J
Reshetikhin, N
[J]. TOPOLOGY, 1996, 35 (04) : 1069 - 1083
[5] [Anonymous], 1998, GRUNDLEHREN MATH WIS
[6] Carter R., 2005, ALGEBRAS FINITE AFFI
[7] Topological field theory interpretation of string topology
Cattaneo, AS
Fröhlich, J
Pedrini, B
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 240 (03) : 397 - 421
[8] Higher-dimensional B F theories in the Batalin-Vilkovisky formalism:: The BV action and generalized Wilson loops
Cattaneo, AS
Rossi, CA
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2001, 221 (03) : 591 - 657
[9] Chas M, 2004, LEGACY OF NIELS HENRIK ABEL, P771
[10] Chas Moira., 1999, STRING TOPOLOGY

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