Algebraic structures on parallelizable manifolds

Authors

Sergey Grigorian, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

11-1-2024

Abstract

In this paper we explore algebraic and geometric structures that arise on parallelizable manifolds. Given a parallelizable manifold L , there exists a global trivialization of the tangent bundle, which defines a map ρ p : l ⟶ T p L for each point p ∈ L , where l is some vector space. This allows us to define a particular class of vector fields, known as fundamental vector fields, that correspond to each element of l . Furthermore, flows of these vector fields give rise to a product between elements of l and L , which in turn induces a local loop structure (i.e. a non-associative analog of a group). Furthermore, we also define a generalization of a Lie algebra structure on l . We will describe the properties and examples of these constructions.

Comments

Original published version available at https://doi.org/10.1016/j.jalgebra.2024.06.001

Recommended Citation

Grigorian, Sergey. 2024. “Algebraic Structures on Parallelizable Manifolds.” Journal of Algebra 657: 804–39. https://doi.org/10.1016/j.jalgebra.2024.06.001

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Journal of Algebra

DOI

https://doi.org/10.1016/j.jalgebra.2024.06.001