Geodesic
Isotopic pairs and their representations
Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 1, pp. 18-28 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper presents representations of isotopic pairs, the algebraic objects which can, probably, be convenient for describing some forms of the non-Hamiltonian interaction of Hamiltonian systems on the quantum level. General constructions are illustrated by simple examples. 
@article{TMF_1995_105_1_a1,
     author = {D. V. Yur'ev},
     title = {Isotopic pairs and their representations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {18--28},
     year = {1995},
     volume = {105},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1995_105_1_a1/}
}
TY  - JOUR
AU  - D. V. Yur'ev
TI  - Isotopic pairs and their representations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1995
SP  - 18
EP  - 28
VL  - 105
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1995_105_1_a1/
LA  - ru
ID  - TMF_1995_105_1_a1
ER  - 
%0 Journal Article
%A D. V. Yur'ev
%T Isotopic pairs and their representations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1995
%P 18-28
%V 105
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1995_105_1_a1/
%G ru
%F TMF_1995_105_1_a1
D. V. Yur'ev. Isotopic pairs and their representations. Teoretičeskaâ i matematičeskaâ fizika, Tome 105 (1995) no. 1, pp. 18-28. http://geodesic.mathdoc.fr/item/TMF_1995_105_1_a1/

[1] Juriev D., Topics in nonhamiltonian (magnetic-type) interaction of classical hamiltonian dynamic systems. I, solv-int/9505001

[2] Santilli R.M., Foundations of theoretical mechanics. II. Birkhoffian generalization of Hamiltonian mechanics, Springer-Verlag, 1982 | MR

[3] Juriev D., Topics in hidden symmetries, hep-th/9405050 | MR

[4] Faulkner J.R., J. Alg., 26 (1973), 1–9 ; Faulkner J.R., Ferrar J.C., Commun. Alg., 8 (1980), 993–1013 | DOI | MR | Zbl | DOI | MR | Zbl

[5] Okubo S., Jordan triple systems and Yang-Baxter equation, Preprint Univ. Rochester UR-1334, ER-40685-783, 1993 ; hep-th/9312181 | MR

[6] Loos O., Jordan pairs, Springer-Verlag, 1975 ; McCrimmon K., Bull. Amer. Math. Soc., 84 (1978), 612–627 | MR | Zbl | DOI | MR | Zbl

[7] Biedenham L.C., Truini P., J. Math. Phys., 23 (1982), 1327–1345 | DOI | MR

[8] Meyberg K., Math. Z., 115 (1970), 58 ; Jacobson N., “Structure and representations of Jordan algebras”, Amer. Math. Soc., RI (1971) ; Koecher M., Lectures at the Rhine-Westfalia Academy of Sciences, 307, WestDeutscher Verlag, Opladen, 1982 | DOI | MR | Zbl | MR | MR

[9] Klimyk A.U., Santilli R.M., Alg. Groups Geom., 10 (1993), 323–333 | MR

[10] Fuks D.B., Kogomologii beskonechnomernykh algebr Li, Nauka, M., 1984 | MR

[11] Okubo S., J. Math. Phys., 34 (1993), 3292–3315 | DOI | MR | Zbl

[12] Dixmier J., Algebres enveloppantes, Gauthier-Villars, Paris, 1973 | MR

[13] Kirillov A.A., Elementy teorii predstavlenii, Nauka, M., 1972 | MR

[14] Wigner E.P., Phys. Rev., 77 (1950), 711–712 | DOI | MR | Zbl

[15] Palev T.D., J. Math. Phys., 23 (1982), 1778–1784 | DOI | MR | Zbl

[16] Green H.S., Phys. Rev., 90 (1953), 270–273 ; Говорков А.Б., ЖЭТФ, 54 (1968), 1785–1798; Ohnuki Y., Kamefuchi S., Quantum field theory and parastatistics, Springer-Verlag, 1982 ; Okubo S., J. Math. Phys., 35 (1994), 2785–2803 | DOI | MR | Zbl | MR | Zbl | DOI | MR | Zbl

[17] Yang L.M., Phys. Rev., 84 (1951), 788–790 | DOI | Zbl