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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
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
Download citation
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
eBook Packages: Springer Book Archive