Graded and non-associative algebras and their applications in physics

MAM intensive research course for PhD students and researchers.
MAM research frontier lecture series.

September 25,Wednesday,

Lecture 1-2: 15.15-17.00, 

Coffee break, 17.00-17.10

Lecture 3: 17.10-18.00

Location: U3-083 (Hilbert room), Västerås, Mälardalen University


Professor em Richard Kerner,

Laboratoire De Physique Théorique De La Matière Condensée, Sorbonne-Université, Paris, France
and Physics, University of Paris-VI



Z3-Graded and non-associative algebras and their applications in physics

The first lecture will be an introduction to Z3-graded generalizations of Grassmann and Clifford algebras. The second one will be devoted to Z3-graded generalization of exterior calculus in differential geometry. The third one will be devoted to physical applications: generalized gauge theories, generalized Pauli's principle, generalized Lorentz algebra.


Recommended references: 

R. Kerner, Ternary Z2 and Z3 Graded Algebras and Generalized Color Dynamics, Mathematical Structures and Applications: In Honor of Mahouton Norbert Houkonnou 60th birthday, Springer, 2018, 311-357

R. Kerner, Ternary and non-associative structures, International Journal of Geometric Methods in Modern Physics 5 (08), 2008, 1265-1294,

V Abramov, R Kerner, B Le Roy, Hypersymmetry: A Z3-graded generalization of supersymmetry, Journal of Mathematical Physics 38 (3), 1997, 1650-1669

L Vainerman, R Kerner, On special classes of n‐algebras, Journal of Mathematical Physics 37 (5), 1996, 2553-2565,

R Kerner, The cubic chessboard, Classical and Quantum Gravity 14 (1A), 1997, A203

R. Kerner, Ternary algebraic structures and their applications in physics, 2000, arXiv preprint math-ph/0011023

R Kerner, Ternary generalization of Heisenberg's algebra, Journal of Physics: Conference Series 624 (1), 2015, 012021

R Kerner, Z3 ‐graded algebras and the cubic root of the supersymmetry translations, Journal of mathematical physics 33 (1), 1992, 403-411

R. Kerner, “Z3-graded algebras and the cubic root of the supersymmetry translations,” J. Math. Phys. 33, 403–411 (1992). 

R. Kerner, “Z3-grading and ternary algebraic structures,” in Symmetries in Science, VI (Plenum, New York, 1993), p. 373.

R. Kerner, “Ternary structures and Z3-grading,” in Generalized Symmetries in Physics, edited by H. D. Doebner V. Dobrev, and A. U. Ushveridze (World Scientific, Singapore, 1994), pp. 375–394.

R. Kerner, Zn-graded differential calculus, Czechoslovak Journal of Physics 47 (1), 1997, 33-40