Differential graded Lie groups and their differential graded Lie algebras
Abstract
In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to differential graded Lie groups (DGLG). We first recall the classical problem of integration in the context, and present the construction for (nongraded) differential Lie algebras. Then, we define the category of differential graded Lie groups and study its properties. We show how to associate a differential graded Lie algebra to every differential graded Lie group and viceversa. For the DGLA $\to$ DGLG direction, the main ``tools'' are graded Hopf algebras and HarishChandra pairs (HCP)  we define the category of graded and differential graded HCPs and explain how those are related to the desired construction. We describe some near at hand examples and mention possible generalizations.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.09630
 Bibcode:
 2019arXiv190609630J
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Algebraic Geometry
 EPrint:
 46 pages