INTERNAL SYMMETRY GROUPS OF CUBIC ALGEBRAS

被引：12

作者：

Kerner, Richard ^{[1
]}

Suzuki, Osamu ^{[2
]}

机构：

[1] Univ Paris 06, CNRS, UMR 7600, Lab Phys Theor Mat Condensee, F-75005 Paris, France

[2] Nihon Univ, Coll Humanities & Sci, Dept Comp Sci & Syst Anal, Setagaya Ku, Tokyo 1568550, Japan

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2012年 / 9卷 / 06期

关键词：

Pauli's principle; Z(3)-symmetry; ternary and cubic algebras; cubic Dirac equation; SUPERSYMMETRY; STABILITY; MATTER;

D O I：

10.1142/S0219887812610075

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate certain Z(3)-graded associative algebras with cubic Z(3) invariant constitutive relations, introduced by one of us some time ago. The invariant forms on finite algebras of this type are given in the cases with two and three generators. We show how the Lorentz symmetry represented by the SL(2, C) group can be introduced without any notion of metric, just as the symmetry of Z(3)-graded cubic algebra and its constitutive relations. Its representation is found in terms of the Pauli matrices. The relationship of such algebraic constructions with quark states is also considered.

引用

页数：10

共 15 条

[1] Hypersymmetry: A Z(3)-graded generalization of supersymmetry [J].