Integration of quadratic Lie algebroids to Riemannian Cartan-Lie groupoids

Autor(es)

Kotov, Alexei ; Strobl, Thomas

• Tipo de documento: Artigo Científico
• Fonte: LETTERS IN MATHEMATICAL PHYSICS; v. 108, n. 3, p. 20-pg., 2018-03-01.

Resumo

Cartan-Lie algebroids, i.e., Lie algebroids equipped with a compatible connection, permit the definition of an adjoint representation, on the fiber as well as on the tangent of the base. We call (positive) quadratic Lie algebroids, Cartan-Lie algebroids with ad-invariant (Riemannian) metrics on their fibers and base and g, respectively. We determine the necessary and sufficient conditions for a positive quadratic Lie algebroid to integrate to a Riemannian Cartan-Lie groupoid. Here we mean a Cartan-Lie groupoid equipped with a bi-invariant and inversion-invariant metric on such that it induces by submersion the metric g on its base and its restriction to the t-fibers coincides with . (AU)

• Processo FAPESP: 11/11973-4 - ICTP Instituto Sul-Americano para Pesquisa Fundamental: um centro regional para física teórica
• Beneficiário: Nathan Jacob Berkovits
• Modalidade de apoio: Auxílio à Pesquisa - Temático