Family Of Lie Groups Research Articles

Discovering sparse representations of Lie groups with machine learning

Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras. We show that our method reproduces the canonical (sparse) representations of the generators of the Lorentz group, as well as the U(n) and SU(n) families of Lie groups. This approach is completely general and can be used to find the infinitesimal generators for any Lie group.

Geometric characteristics and properties of a three-parametric family of Lie groups with almost contact B-metric structure of the smallest dimension

Almost contact [Formula: see text]-metric manifolds of the lowest dimension 3 are constructed by a three-parametric family of Lie groups. Our aim is to determine the class of considered manifolds in a classification of almost contact [Formula: see text]-metric manifolds and their most important geometric characteristics and properties. Also, the type of the constructed Lie algebras is established in the Bianchi classification.

Lie groups as 3-dimensional almost paracontact almost paracomplex Riemannian manifolds

Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension 3 are considered. Such structures are constructed on a family of Lie groups and the obtained manifolds are studied. Curvature properties of these manifolds are investigated. An example is commented as support of obtained results.

Riemannian Geometry of Two Families of Tangent Lie Groups

Using vertical and complete lifts, any left invariant Riemannian metric on a Lie group induces a left invariant Riemannian metric on the tangent Lie group. In the present article we study the Riemannian geometry of tangent bundle of two families of Lie groups. The first one is the family of special Lie groups considered by J. Milnor and the second one is the class of Lie groups with one-dimensional commutator groups. The Levi-Civita connection, sectional and Ricci curvatures have been investigated.