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Ternary symmetries and the Lorentz group

Richard Kerner (2011)

Banach Center Publications

We show that the Lorentz and the SU(3) groups can be derived from the covariance principle conserving a Z₃-graded three-form on a Z₃-graded cubic algebra representing quarks endowed with non-standard commutation laws. The ternary commutation relations on an algebra generated by two elements lead to cubic combinations of three quarks or antiquarks that transform as Lorentz spinors, and binary quark-anti-quark combinations that transform as Lorentz vectors.

The differential form method for finding symmetries.

Harrison, B.Kent (2005)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The geometry of the octet

Louis Michel, Luigi A. Radicati (1973)

Annales de l'I.H.P. Physique théorique

The heat kernel on Lie groups.

Nicholas Th. Varopoulos (1996)

Revista Matemática Iberoamericana

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

Let $A, B$ denote generic binary forms, and let $𝔲_{r} = {(A, B)}_{r}$ denote their $r$ -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the ${𝔲_{r}}$ . As a consequence, we show that each of the higher transvectants ${𝔲_{r} : r \geq 2}$ is redundant in the sense that it can be completely recovered from $𝔲_{0}$ and $𝔲_{1}$ . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of $S L_{2}$ -representations, and the...