Multiplicativity, from Lie groups to generalized geometry

TL;DR

This paper surveys the concept of multiplicativity across Lie groups, Lie groupoids, and Lie algebroids, highlighting its role in Poisson geometry and generalized geometry.

Contribution

It provides a comprehensive overview of multiplicativity from classical Poisson-Lie groups to modern generalized geometric structures.

Findings

Unified perspective on multiplicativity in various geometric contexts

Connections between Lie groupoids, algebroids, and generalized geometry

Insights into the infinitesimal and global aspects of multiplicative structures

Abstract

We survey the concept of multiplicativity from its initial appearance in the theory of Poisson-Lie groups to the far-reaching generalizations, for multivectors and differential forms in the geometry and the generalized geometry of Lie groupoids, as well as their infinitesimal counterparts in the theory of Lie algebroids.