Real representations of finite Clifford algebras. 1. Classification

Okubo, Susumu

doi:10.1063/1.529277

Real representations of finite Clifford algebras. 1. Classification

Susumu Okubo
(
- Rochester U.
)

Aug, 1990

43 pages

Published in:

J.Math.Phys. 32 (1991) 1657-1668

DOI:

10.1063/1.529277

Report number:

UR-1183,
ER-13065-639

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Abstract: (AIP)

A classification of real matrix irreducible representations of finite‐dimensional real Clifford algebras has been made. In contrast to the case of complex representation, three distinct types of representations can be obtained which we call normal, almost complex, and quaternionic. The dimension of the latter two cases is twice as large as that of the normal representation. A criteria for a given Clifford algebra to possess a particular type of the representations is also given with some applications.

References(9)

Figures(0)

- Topology 3 3

Realization, Classification, and Extension of Certain Physically Important Groups and Algebras

Nikos Salingaros
(
- Massachusetts U., Boston
)

- J.Math.Phys. 22 (1981) 226
•
DOI:
- 10.1063/1.524893

On the Classification of Clifford Algebras and Their Relation to Spinors in $n$ Dimensions

Nikos Salingaros
(
- Iowa U.
)

- J.Math.Phys. 23 (1982) 1,
- J.Math.Phys. 23 (1982) 1231 (erratum)
•
DOI:
- 10.1063/1.525192

On the Classification of Clifford Algebras and Their Relation to Spinors in $n$ Dimensions

Nikos Salingaros
(
- Iowa U.
)

- J.Math.Phys. 23 (1982) 1,
- J.Math.Phys. 23 (1982) 1231 (erratum)
•
DOI:
- 10.1063/1.525192

- Gen.Rel.Grav. 21 21

Supersymmetry, Supergravity Theories and the Dual Spinor Model

F. Gliozzi
(
- Ecole Normale Superieure
)
,
Joel Scherk
(
- Ecole Normale Superieure
)
,
David I. Olive
(
- CERN and
- Bohr Inst.
)

- Nucl.Phys.B 122 (1977) 253-290,
- In *Schwarz, J.H. (ed.): Superstrings, Vol. 1*, 300-337,
- In *Ferrara, S. (ed.): Supersymmetry, Vol. 2*, 1209-1246,
- In *Schellekens, A.N. (ed.): Superstring construction* 33-70
•
DOI:
- 10.1016/0550-3213(77)90206-1

Statistical theory of the energy levels of complex systems. I

F.J. Dyson

- J.Math.Phys. 3 (1962) 140-156
•
DOI:
- 10.1063/1.1703773

- J.Math.Phys. 3 157

Properties of the Dirac matrices

R.H. Good
(
- Penn State U.
)

- Rev.Mod.Phys. 27 (1955) 187-211
•
DOI:
- 10.1103/RevModPhys.27.187

Real representations of finite Clifford algebras. 1. Classification

Citations per year

Realization, Classification, and Extension of Certain Physically Important Groups and Algebras

On the Classification of Clifford Algebras and Their Relation to Spinors in nnn Dimensions

On the Classification of Clifford Algebras and Their Relation to Spinors in nnn Dimensions

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Statistical theory of the energy levels of complex systems. I

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On the Classification of Clifford Algebras and Their Relation to Spinors in $n$ Dimensions

On the Classification of Clifford Algebras and Their Relation to Spinors in $n$ Dimensions