nLab Lie algebra contraction

Idea

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

Related concepts

• Penrose limit

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)