From Wigner--In{\"o}n{\"u} Group Contraction to Contractions of Algebraic Structures

TL;DR

This paper reviews the concept of group contraction, emphasizing degenerate transformations and their importance in solving problems in mathematical physics through algebraic structure contractions.

Contribution

It provides a comprehensive review of group contraction theory and highlights its significance in algebraic structures relevant to mathematical physics.

Findings

Highlights the role of degenerate transformations in group contractions

Connects algebraic contractions to solvable problems in physics

Emphasizes the historical development of the contraction concept

Abstract

The development of the notion of group contraction first introduced by E. In{\"o}n{\"u} and E.P. Wigner in 1953 is briefly reviewed. The fundamental role of the idea of degenerate transformations is stressed. The significance of contractions of algebraic structures for exactly solvable problems of mathematical physics is noticed.