What is a double cover of a group?

Double coverage, a defensive strategy in American football, basketball, and other sports. Being covered by more than one health insurance plan. A type of Asphalt roll roofing.

What does double cover mean?

In gridiron football double coverage is a state of defensive playcalling wherein two defensive players are assigned to “cover” one offensive player. This situation is often seen with standout wide receivers and running backs. It is extremely rare to have two defensive backs man-cover a single receiver.

What does it take to be a theoretical physicist?

Becoming a theoretical physicist usually requires a doctorate in physics or mathematics, post-doctoral experience, and several years of job experience applying physics. A theoretical physicist, sometimes called a mathematical physicist, uses only theories and math to predict observations, like natural events.

How is Lie algebra used in physics?

In physics, Lie groups appear as symmetry groups of physical systems, and their Lie algebras (tangent vectors near the identity) may be thought of as infinitesimal symmetry motions. Thus Lie algebras and their representations are used extensively in physics, notably in quantum mechanics and particle physics.

Is a circle a Lie group?

A Lie group is first of all a group. Secondly it is a smooth manifold which is a specific kind of geometric object. The circle and the sphere are examples of smooth manifolds. Informally, a Lie group is a group of symmetries where the symmetries are continuous.

Why is S2 not a Lie group?

Since χ(S2) = 2, it can’t admit a Lie group structure. More generally, χ(S2n) = 0 for n ≥ 1, so S2n can’t be Lie groups.

Why is Lie algebra important physics?

Here is a brief answer: Lie groups provide a way to express the concept of a continuous family of symmetries for geometric objects. Most, if not all, of differential geometry centers around this. By differentiating the Lie group action, you get a Lie algebra action, which is a linearization of the group action.