2019/06/23 by Benoît Jubin, Alexei Kotov, Jubin, Benoit +5 · 3 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Carbohydrate Chemistry and Synthesis #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Sphingolipid Metabolism and Signaling
paper · pdf · doi:10.48550/arxiv.1906.09630
openalex publication_date 2019/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (non-graded) 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 vice-versa. For the DGLA → DGLG direction, the main ``tools'' are graded Hopf algebras and Harish-Chandra 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.