Algebraic Constructions in the Category of Lie Algebroids
By C. Arcuş. 2011
138 citations recorded by the source corpus.
A generalized notion of a Lie algebroid is presented. Using this, the Lie algebroid generalized tangent bundle is obtained. A new point of view over (linear) connections theory on a fiber bundle is presented. These connections are characterized by o horizontal distribution of the Lie algebroid generalized tangent bundle. Some basic properties of these generalized connections are investigated. Special attention to the class of linear connections is paid. The recently studied Lie algebroids connections can be recovered as special cases within this more general framework. In particular, all results are similar with the classical results. Formulas of Ricci and Bianchi type and linear connections of Levi-Civita type are presented.
Subfields: Algebra and Number Theory, Astronomy and Astrophysics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/866f53238a12a274cbb30fa3ff8ca7b274e8fd45
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In Algebra and Number Theory
- C. A. Abad
- M. Crainic
- E. Meinrenken
- David Li-Bland
- R. Mehta
- A. Gracia-Saz
- H. Bursztyn
- Rui Loja Fernandes
In Astronomy and Astrophysics
In Statistical and Nonlinear Physics
Citations in the corpus
- Lectures on integrability of Lie brackets (2006, unknown): “The theory of connections played a large motivation in Mackenzie’s approach to Lie groupoid”
- Representations up to homotopy of Lie algebroids (2009, background): “Recall [23] that the pull-back algebroid τ A has the fiber at x ∈ N :”
- Courant Algebroids and Poisson Geometry (2008, methodology): “We introduce the notion of an action of a Courant algebroid A → N on a manifold M , similar to the HigginsMackenzie definition of a Lie algebroid action [15].”