O'Reilly logo

Lie Groups, Physics, and Geometry by Robert Gilmore

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

5

Matrix algebras

 

 

The Lie algebras of the matrix Lie groups described in Chapter 3 are constructed. This is done by linearizing the constraints defining these matrix groups in the neighborhood of the identity operation.

5.1 Preliminaries

Lie algebras for the matrix groups treated in Chapter 3 are computed by linearizing the defining conditions in the neighborhood of the identity. The general linear groups GL(n; images) have no defining condition (the only condition is det(M) ≠ 0), while Examples (2)–(7) are already defined by linear constraints. Examples (8)–(11) are defined by bilinear and quadratic constraints that are linearized by applying the ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required