Multiplicative forms at the infinitesimal level

By H. Bursztyn, A. Cabrera. 2010

77 citations recorded by the source corpus.

We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known integration results related to Poisson geometry. We also revisit multiplicative multivector fields and their infinitesimal counterparts, drawing a parallel between the two theories.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c4e26574ca4f7960765fd72981b8ef2a8b3b874b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Rui Loja Fernandes
2. M. Crainic
3. Matías L. del Hoyo
4. I. Struchiner
5. M. A. Salazar
6. R. Mehta
7. A. Gracia-Saz
8. C. A. Abad

In Mathematical Physics

1. Rui Loja Fernandes
2. M. Crainic
3. Matías L. del Hoyo
4. I. Struchiner
5. M. A. Salazar
6. R. Mehta
7. A. Gracia-Saz
8. C. A. Abad

In Statistical and Nonlinear Physics

1. M. Crainic
2. I. Struchiner
3. Matías L. del Hoyo
4. Rui Loja Fernandes
5. M. A. Salazar
6. R. Mehta
7. A. Gracia-Saz

Citations in the corpus

• Multiplicative forms and Spencer operators (2012, background): “Rewriting everything in terms of ν and α we obtain the result of [3, 8]:”
• Riemannian metrics on Lie groupoids (2014, background): “G([3]) x G (h1, h2, h3) · k = (h1k, h2k, h3k).”