Manin triples for double Lie bialgebroids
Ana Carolina Man\c{c}ur
TL;DR
This paper establishes a correspondence between double Lie bialgebroids and LA-Manin triples using LA-Courant algebroids, linking algebraic structures with geometric integration and differentiation methods.
Contribution
It introduces LA-Manin triples as a framework for double Lie bialgebroids and connects LA-Courant algebroids with Drinfeld doubles through integration and differentiation.
Findings
LA-Courant algebroids provide the Manin triple framework for double Lie bialgebroids
A correspondence between double Lie bialgebroids and LA-Manin triples is established
LA-Courant algebroids and CA-groupoids from Drinfeld doubles are related via integration and differentiation
Abstract
We verify that LA-Courant algebroids provide the Manin triple framework for double Lie bialgebroids. Specifically, we establish a correspondence between double Lie bialgebroids and LA-Manin triples, i.e., LA-Courant algebroids equipped with a pair of complementary LA-Dirac structures. As an application, LA-Courant algebroids and CA-groupoids given by Drinfeld doubles are shown to correspond via integration and differentiation.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models