Unitary Left Multiplication in Indefinite Unitary Groups: Sp(1,1) in SU(2,2), Its Absence in SU(1,3), and the Role of Dimension Four

Unitary left multiplication lies in Sp(2) in SU(4) and in Sp(1,1) in SU(2,2), but has no symplectic analogue in SU(1,3), where complex boosts take its place. We also show why the Gram–Schmidt-free construction works only in dimension four.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23878623
Primary Topic
Advanced Algebra and Geometry
Type
article
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article

Unitary Left Multiplication in Indefinite Unitary Groups: Sp(1,1) in SU(2,2), Its Absence in SU(1,3), and the Role of Dimension Four

Sung-tae Lim
1 links
Zenodo (CERN European Organization for Nuclear Research)
Advanced Algebra and Geometry
article

Unitary Left Multiplication in Indefinite Unitary Groups: Sp(1,1) in SU(2,2), Its Absence in SU(1,3), and the Role of Dimension Four

Sung-tae Lim
article en

Abstract

Unitary left multiplication lies in Sp(2) in SU(4) and in Sp(1,1) in SU(2,2), but has no symplectic analogue in SU(1,3), where complex boosts take its place. We also show why the Gram–Schmidt-free construction works only in dimension four.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 12%
Advanced Algebra and Geometry
DOIOpen Access PDFOpenAlex
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Unitary Left Multiplication in Indefinite Unitary Groups: Sp(1,1) in SU(2,2), Its Absence in SU(1,3), and the Role of Dimension Four — Sung-tae Lim · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS