An alternative interpretation of the Beltrametti–Blasi formula by means of differential forms

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“…To show that Tr M 6 and Tr M 8 are, respectively, a sixth and eight order Casimir operator of F 4 , we can make use of the analytical approach to the invariant problem [16,17]. Actually, in both cases it suffices to show that…”

“…In order to be useful for the labelling of representations, we need n = 4 subgroup scalars Θ [p,q] , which must commute with each other to avoid interaction. The problem of finding adequate combinations of labelling operators for general reduction of groups is still an unsolved one, although some criteria and methods have been developed to avoid direct computation [17,21]. Even for degenerate representations 8 , which usually require less labels, no general method has been developed yet.…”

Complete Labeling of G 2-Representations

“…2 Another possible procedure to show that Tr[M 6 ] is a Casimir operator is to realize the generators {H 1 , H 2 , E i , F i , T i , S i } by means of differential operators and verify that they satisfy the corresponding system of PDEs [1,[11][12][13][14].…”

Quasi-Classical Lie Algebras and their Contractions

“…In this sense, the equations of motion of the Yang-Mills equations of g can be recovered from the limit (for t → ∞) of the equations of motion (4) corresponding to g. It is interesting that by this contraction procedure, we can obtain a large hierarchy of Lagrangians corresponding to non-isomorphic Lie algebras, starting from a suitable Lie algebra. 1 To illustrate this fact, consider the contraction so(3, 1) g α=0,η≥2 6,93 of the Lorentz algebra onto the quasi-classical solvable Lie algebra g 0,η 6,93 (see Table 2). We choose a basis {X 1 , .…”