Cayley-Klein Algebras as Graded Contractions of so(N+1)

TL;DR

This paper explores graded contractions of the Lie algebra so(N+1), highlighting Cayley-Klein algebras as a significant subset, thereby advancing understanding of algebraic structures through contraction techniques.

Contribution

It introduces a systematic study of Z_2^{⊗N} graded contractions of so(N+1), identifying Cayley-Klein algebras as a naturally distinguished subset.

Findings

Cayley-Klein algebras are characterized within graded contractions.

The structure of graded contractions of so(N+1) is clarified.

New connections between algebraic contractions and Cayley-Klein algebras are established.

Abstract

We study $\Bbb Z_2^{\otimes N}$ graded contractions of the real compact simple Lie algebra $so(N+1)$, and we identify within them the Cayley-Klein algebras as a naturally distinguished subset.