Octonionic representations of GL(8,scr(R)) and GL(4,scr(C))

Journal Article · Sat Feb 01 04:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531879· OSTI ID:463527

De Leo, S ^[1]; Abdel-Khalek, K ^[2]

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1. Dipartimento di Fisica, Universita di Lecce and Instituto Nazionale di Fisica Nucleare, Sezione di Lecce, Lecce, 73100 (Italy)
2. International Centre for Theoretical Physics, I-34100 Trieste (Italy)

Octonionic algebra being nonassociative is difficult to manipulate. We introduce left/right octonionic barred operators which enable us to reproduce the associative GL(8,scr(R)) group. Extracting the basis of GL(4,scr(C)), we establish an interesting connection between the structure of left/right octonionic barred operators and generic 4{times}4 complex matrices. As an application we give an octonionic representation of the four-dimensional Clifford algebra. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 463527
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CLIFFORD ALGEBRA
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
QUANTUM MECHANICS
SU GROUPS