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Topics in isotopic pairs and their representations. II. A general supercase
Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 1, pp. 149-158 Cet article a éte moissonné depuis la source Math-Net.Ru

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Isotopic pairs, algebraic objects, which are convenient to describe certain forms of non-Hamiltonian (magnetic-type) interaction of Hamiltonian systems on the quantum level, are considered in the general framework of the vector superalgebra. 
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D. V. Yur'ev. Topics in isotopic pairs and their representations. II. A general supercase. Teoretičeskaâ i matematičeskaâ fizika, Tome 111 (1997) no. 1, pp. 149-158. http://geodesic.mathdoc.fr/item/TMF_1997_111_1_a11/

[1] D. V. Yurev, TMF, 105:1 (1995), 18–28 | MR | Zbl

[2] F. A. Berezin, Vvedenie v algebru i analiz ot kommutiruyuschikh i antikommutiruyuschikh peremennykh, Nauka, M., 1983 ; Д. А. Лейтес, УМН, 35:1 (1980), 3–57 ; Ю. И. Манин, Калибровочные поля и комплексная геометрия, Наука, М., 1984 ; В. И. Огиевецкий, Е. С. Сокачев, Матем. анализ, 22, ВИНИТИ, М., 1984, 137–173 ; А. А. Рослый, О. М. Худавердян, А. С. Шварц, Соврем. пробл. матем. Фундам. направления, 9, ВИНИТИ, М., 1986, 247–284 | MR | Zbl | MR | Zbl | MR | Zbl | MR | MR

[3] D. Juriev, Russian J. Math. Phys., 5 (1997) (to appear) , [e-version: funct-an/9409003] ; On the dynamics of noncanonically coupled oscillators and its hidden superstructure, Preprint ESI 167, 1994; E-print solv-int/9503003 | MR | Zbl

[4] A. G. Kurosh, Obschaya algebra, Nauka, M., 1974 | MR | Zbl

[5] D. Juriev, On the nonHamiltonian interaction of two rotators, Report RCMPI/95-01, 1995; E-print dg-ga/9409004

[6] M. Koecher, Jordan algebras and their applications, Acad. Press, N.Y., 1962 ; N. Jacobson, Structure and representations of Jordan algebras, Providence Amer. Math. Soc., Providence, 1968 ; M. Koecher, An elementary approach to bounded symmetric domains, Univ. Press, Houston, 1969 ; О. Лоос, Симметрические пространства, Наука, М., 1985 | MR | MR | Zbl | MR | Zbl | MR

[7] O. Loos, Jordan pairs, Springer-Verlag, 1975 ; Е. Н. Кузьмин, И. П. Шестаков, Соврем. пробл. матем. Фундам. направления, 57, ВИНИТИ, М., 1992 | MR

[8] J. R. Faulkner, J. C. Ferrar, Commun. Alg., 8 (1980), 993–1013 | DOI | MR | Zbl

[9] D. Juriev, Topics in hidden symmetries, , 1994 E-print hep-th/9405050

[10] D. V. Yurev, Fundam. prikl. matem., 2 (1996) (to appear) ; E-print funct-an/9411007 | Zbl

[11] D. A. Leites, Sovrem. probl. matem. Noveishie dostizheniya, 25, VINITI, M., 1984, 3–50 | MR

[12] A. Gisharde, Kogomologii topologicheskikh grupp i algebr Li, Mir, M., 1984 | MR

[13] D. P. Zhelobenko, UMN, 17:1 (1962), 27–120 ; J. Mickelsson, Rep. Math. Phys., 4 (1973), 303–318 ; 18 (1980), 197–210 ; A. Homberg, Invent. Math., 37 (1975), 42–47 ; Д. П. Желобенко, Изв. АН СССР, сер. матем., 52 (1988), 758–773 ; D. P. Zhelobenko, J. Group Theory Phys., 1 (1993), 201–233; Д. П. Желобенко, Представления редуктивных алгебр Ли, Наука, М., 1994 | MR | DOI | MR | DOI | MR | Zbl | MR | MR

[14] R. M. Asherova, Yu. F. Smirnov, V. N. Tolstoi, TMF, 8 (1971), 255–271 ; Матем. заметки, 26:1 (1979), 15–25 ; В. Н. Толстой, Теоретико-групповые методы в физике, Т. 2, Наука, М., 1986, 46–54 | MR | Zbl | MR | Zbl | MR

[15] S. Okubo, J. Math. Phys., 35 (1994), 2785–2803 | DOI | MR | Zbl

[16] M. A. Semenov-Tyan-Shanskii, Funkts. analiz i ego prilozh., 13:4 (1983), 17–33 | MR

[17] D. P. Zhelobenko, A. I. Shtern, Predstavleniya grupp Li, Nauka, M., 1983 | MR

[18] N. N. Bogolyubov, V. V. Tolmachev, D. V. Shirkov, Novyi metod v teorii sverkhprovodimosti, Izd-vo AN SSSR, M., 1958

[19] A. Barut, R. Ronchka, Teoriya predstavlenii grupp i ee prilozheniya, Mir, M., 1980 | MR | Zbl

[20] M. V. Karasev, V. P. Maslov, Nelineinye skobki Puassona. Geometriya i kvantovanie, Nauka, M., 1991 | MR | Zbl

[21] V. Nazaikinskii, B. Sternin, V. Shatalov, Methods of noncommutative analysis: theory and applications, Walter de Gruyter Inc., 1995 | MR

[22] V. E. Korepin, L. D. Faddeev, TMF, 25 (1975), 147–163 ; L. D. Faddeev, V. E. Korepin, Phys. Rep., 42:1 (1978) | MR | DOI | MR

[23] V. G. Drinfeld, Zap. nauchn. semin. LOMI, 155, 1986, 18–49 ; Н. Ю. Решетихин, Л. А. Тахтаджян, Л. Д. Фаддеев, Алгебра и анализ, 1 (1989), 178–206 ; А. П. Исаев, ЭЧАЯ, 26:5 (1995), 1204–1263 | Zbl | MR

[24] A. Gerasimov, S. Khoroshkin, D. Lebedev, A. Morozov, Generalized Hirota equations and representation theory. I: The case of $\operatorname{SL}(2)$ and $\operatorname{SL}_q(2)$, , 1994 ; A. Mironov, Quantum deformations of $\tau$-functions, bilinear identities and representation theory, , 1994 ; S. Kharchev, A. Mironov, A. Morozov, Non-standard KP evolution and quantum $\tau$-functions, , 1995 E-print hep-th/9405011E-print hep-th/9409190E-print q-alg/9501013 | MR | MR

[25] P. Lax, Commun. Pure Appl. Math., 21 (1968), 467–490 ; J. Moser, Adv. Math., 16 (1975), 197–220 ; В. Е. Захаров, А. Б. Шабат, Функц. анализ и его прилож., 8:3 (1974), 43–53 ; 13:3 (1979), 13–22 ; Б. А. Дубровин, В. Б. Матвеев, С. П. Новиков, УМН, 31:1 (1976), 55–136 ; В. Е. Захаров, С. В. Манаков, С. П. Новиков, Л. П. Питаевский, Теория солитонов. Метод обратной задачи, Наука, М., 1980 | DOI | MR | Zbl | DOI | MR | Zbl | MR | Zbl | MR | Zbl | MR | Zbl | MR | Zbl

[26] A. M. Perelomov, Integriruemye sistemy klassicheskoi mekhaniki i algebry Li, Nauka, M., 1990 | Zbl

[27] D. Juriev, Russian J. Math. Phys., 3:4 (1995), 453–460 ; , 1995 ; Topics in nonHamiltonian (magnetic-type) interactions of classical Hamiltonian dynamical systems. II: Generalized Euler-Ampère equations and Biot-Savart operators, Report RCMPI-96/01, 1996; e-version: mp_arc/95-538 E-print solv-int/9505001 | MR | Zbl | MR

[28] A. P. Veselov, A. B. Shabat, Funkts. analiz i ego prilozh., 27:2 (1993), 1–21 ; А. П. Веселов, С. П. Новиков, УМН, 50:6 (1995), 171–172 | MR | Zbl | MR | Zbl