58 citations · 225 across the 25 of their papers we have counts for
27 papers
Associative half-densities on symplectic groupoids and quantization
Alejandro Cabrera, Gabriel Gonzalo Ledesma Valenotti
In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivate…
Geometric differentiation of simplicial manifolds
Alejandro Cabrera, Matias del Hoyo
We provide a complete geometric solution to the problem of differentiating simplicial manifolds, extending classical Lie theory and complementing existing homotopical and formal ap…
Dimensional reduction of Courant sigma models and Lie theory of Poisson groupoids
Alejandro Cabrera, Miquel Cueca
We show that the 2d Poisson Sigma Model on a Poisson groupoid arises as an effective theory of the 3d Courant Sigma Model associated to the double of the underlying Lie bialgebroid…
Poisson double structures
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We…
Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization
Alejandro Cabrera
This paper contains three results about generating functions for Lie-theoretic integration of Poisson brackets and their relation to quantization. In the first, we show how to cons…
Quotients of multiplicative forms and Poisson reduction
Alejandro Cabrera, Cristian Ortiz
In this paper we study quotients of Lie algebroids and groupoids endowed with compatible differential forms. We identify Lie theoretic conditions under which such forms become basi…