Ternary and Z3-Graded Algebras in Physics

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (15 May 2022) | Viewed by 1628

Special Issue Editor

Laboratory of Theoretical Physics of Condensed Matter, Sorbonne-University and URA CNRS 7600, France
Interests: theoretical and mathematical physics; classical and quantum field theory; elementary particle physics; condensed matter physics (glass and quasicrystals); gravitation and cosmology; mathematical biology; mechanics of continuous media gravitation; particles and fields; condensed matter; mathematical physics

Special Issue Information

Dear Colleagues,

In past decades, Z3-graded algebraical structures have been the object of raising interest, also in view of their possible applications in physics. Numerous generalizations of Z2-graded structures have been proposed and investigated, e.g., Z3-graded exterior differentials and Grassmann algebras, ternary Clifford algebras, Z3-generalizations of supersymmetry, and Z3-graded generalization of spin and color Dirac equation. These topics will be the subject of articles presented in the Special Issue, combining articles of mathematical and physical character.

Prof. Dr. Richard Kerner
Guest Editor

Manuscript Submission Information

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Keywords

  • Z3-graded algebras
  • Ternary Clifford algebras
  • Field theory
  • Hypersymmetry
  • Colour symmetry
  • cubic matrices
  • Z3-graded Lorentz symmetry
  • Color Dirac equation

Published Papers (1 paper)

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Research

13 pages, 272 KiB  
Article
On the Solvability of ℤ3-Graded Novikov Algebras
by Viktor Zhelyabin and Ualbai Umirbaev
Symmetry 2021, 13(2), 312; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13020312 - 13 Feb 2021
Cited by 5 | Viewed by 1032
Abstract
Symmetries of algebraic systems are called automorphisms. An algebra admits an automorphism of finite order n if and only if it admits a Zn-grading. Let N=N0N1N2 be a Z3-graded Novikov [...] Read more.
Symmetries of algebraic systems are called automorphisms. An algebra admits an automorphism of finite order n if and only if it admits a Zn-grading. Let N=N0N1N2 be a Z3-graded Novikov algebra. The main goal of the paper is to prove that over a field of characteristic not equal to 3, the algebra N is solvable if N0 is solvable. We also show that a Z2-graded Novikov algebra N=N0N1 over a field of characteristic not equal to 2 is solvable if N0 is solvable. This implies that for every n of the form n=2k3l, any Zn-graded Novikov algebra N over a field of characteristic not equal to 2,3 is solvable if N0 is solvable. Full article
(This article belongs to the Special Issue Ternary and Z3-Graded Algebras in Physics)
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