nLab
Lie algebra contraction

Contents

Context

Lie theory

∞-Lie theory (higher geometry)

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Contents

Idea

Given a Lie algebra 𝔤\mathfrak{g} over the real numbers or complex numbers, and gives a choice {t 0,t a} aI\{t_0, t_a\}_{a \in I} of linear basis of 𝔤\mathfrak{g}, the corresponding Inönü-Wigner contraction is the Lie algebra obtained by “sending t 0t_0 to zero”, i.e. the Lie algebra obtained from the previous one by passing to basis elements {ϵt 0,t a} aI\{\epsilon t_0, t_a\}_{a \in I} with ϵ\epsilon in the ground field, in the limit that ϵ0\epsilon \to 0.

References

The original article is

  • Erdal İnönü, Eugene Wigner (1953). On the Contraction of Groups and Their Representations. Proc. Nat. Acad. Sci. 39 (6): 510–24.

See also

  • Wikipedia, Group contraction

  • E. J. Saletan, Contraction of Lie Groups. Journal of Mathematical Physics 2: 1–1 (1961)

Created on March 25, 2015 at 11:07:41. See the history of this page for a list of all contributions to it.