Summary
A condition weaker than the ones used in a previous work is proven to imply gradient property of group representations. This same condition guarantees the equivalence between linear and general covariants on a given manifold.
Riassunto
Si dimostra che una condizione piú debole di quelle usate in precedenti lavori è sufficiente per garantire la proprietà gradiente per rappresentazioni di gruppi. Questa stessa condizione garantisce l’equivalenza dei covarianti lineari con i covarianti generici su una determinata varietà.
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References
G. Gaeta andP. Rossi:Nuovo Cimento B,93, 66 (1986).
G. Cicogna, G. Gaeta andP. Rossi:J. Math. Phys. (N. Y.),27, 476 (1986).
D. H. Sattinger:Group Theoretic Methods in Bifurcation Theory, LNM762 (Springer, New York, N. Y., 1979).
D. H. Sattinger:Branching in the Presence of Symmetry (SIAM, Philadelphia, Penn., 1983).
G. Cicogna andG. Gaeta:Phys. Lett. A,116, 303 (1986).
A. Kirillov:Elements de la theorie des representations (MIR, Moscow, 1974).
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Gaeta, G. A weaker condition for gradient property of group representations. Nuovo Cim 96, 147–152 (1986). https://doi.org/10.1007/BF02721468
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DOI: https://doi.org/10.1007/BF02721468