Basic sections of LA-groupoids

2025/11/06 by Antonio Maglio, Maglio, Antonio, Fabricio Valencia +1
Mathematics · #22A22 #58A30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2511.04289

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

We define the notion of basic section of an LA-groupoid whose core-anchor map is injective. Such a notion turns out to be Morita invariant, so that it provides a simpler model for the sections of the stacky Lie algebroids presented by such LA-groupoids, yet equivalent to the well-known model provided by their multiplicative sections.

Citations

• PhD Thesis: Shifted Contact Structures on Differentiable Stacks
• Homological vector fields over differentiable stacks
• Shifted Contact Structures on Differentiable Stacks
• Isometric Lie 2-group actions on Riemannian groupoids
• Contact Dual Pairs
• On the Lie 2-algebra of sections of an LA-groupoid
• Lie Algebroids over Differentiable Stacks
• Jacobi groupoids and generalized Lie bialgebroids
• On symplectic double groupoids and the duality of Poisson groupoids
• Integration of Lie bialgebroids

Related

• On the Lie 2-algebra of sections of an LA-groupoid
• Lie Groupoids
• The Algebroid of a Groupoid in a Tangent Category
• A Functorial Approach to the Infinitesimal Theory of Groupoids
• Proper Cartan Groupoids: Reduction to the Regular Case