Abstract
We investigate some consequences of imposing the Z 3-grading on algebraic structures. It leads to abandoning of algebras defined by binary relations, introducing the ternary relations instead. Possible analogs of Lie algebras and Grassmann algebras are discussed, as well as an example of a simple gauge theory on 3 × 3 matrices. We show also how a cubic root of super-translations can be defined.
Dedicated to Prof. Jan Rzewuski on his 75-th birthday
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© 1993 Springer Science+Business Media Dordrecht
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Kerner, R. (1993). Z 3-Graded Structures. In: Oziewicz, Z., Jancewicz, B., Borowiec, A. (eds) Spinors, Twistors, Clifford Algebras and Quantum Deformations. Fundamental Theories of Physics, vol 52. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1719-7_41
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DOI: https://doi.org/10.1007/978-94-011-1719-7_41
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4753-1
Online ISBN: 978-94-011-1719-7
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