Equivalence of diagonal contractions to generalized IW-contractions with integer exponents

TL;DR

This paper proves that any diagonal contraction of Lie algebras can be represented as a generalized Inönü-Wigner contraction with integer exponents, simplifying the understanding of algebra contractions.

Contribution

The authors provide a simple, rigorous proof that diagonal contractions are equivalent to generalized IW-contractions with integer exponents, clarifying a key aspect of Lie algebra contractions.

Findings

Diagonal contractions are equivalent to integer-exponent generalized IW-contractions

Simplified proof of the equivalence claim by Weimar-Woods

Enhanced understanding of algebra contraction classifications

Abstract

We present a simple and rigorous proof of the claim by Weimar-Woods [Rev. Math. Phys. 12 (2000) 1505-1529] that any diagonal contraction (e.g., a generalized In\"on\"u-Wigner contraction) is equivalent to a generalized In\"on\"u-Wigner contraction with integer parameter powers.