Projective Group Representations in Quaternionic Hilbert Space

TL;DR

This paper extends the theory of projective group representations in quaternionic Hilbert spaces, analyzing associativity, centrality, and generator structures to deepen understanding of their mathematical properties.

Contribution

It introduces a detailed analysis of associativity and centrality conditions for quaternionic projective representations using generator structures.

Findings

Associativity condition formulated via unitary operators

Multi-centrality and centrality analyzed in generator terms

Implications discussed for quaternionic representation theory

Abstract

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi--centrality and centrality assumptions are also analyzed in generator terms, and implications of this analysis are discussed.