Generalized Casimir elements
Izvestiya. Mathematics , Tome 27 (1986) no. 2, pp. 391-400.

Voir la notice de l'article provenant de la source Math-Net.Ru

A method is given for constructing a central element in the universal enveloping algebra $\mathfrak A(L)$ of a Lie algebra $L$, generalizing the method for constructing a Casimir element and not requiring the existence of a nondegenerate invariant form on $L$. Generalized Casimir elements are constructed for certain Lie algebras of Cartan types over a field of positive characteristic. Bibliography: 15 titles.
@article{IM2_1986_27_2_a8,
     author = {A. S. Dzhumadil'daev},
     title = {Generalized {Casimir} elements},
     journal = {Izvestiya. Mathematics },
     pages = {391--400},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a8/}
}
TY  - JOUR
AU  - A. S. Dzhumadil'daev
TI  - Generalized Casimir elements
JO  - Izvestiya. Mathematics 
PY  - 1986
SP  - 391
EP  - 400
VL  - 27
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a8/
LA  - en
ID  - IM2_1986_27_2_a8
ER  - 
%0 Journal Article
%A A. S. Dzhumadil'daev
%T Generalized Casimir elements
%J Izvestiya. Mathematics 
%D 1986
%P 391-400
%V 27
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a8/
%G en
%F IM2_1986_27_2_a8
A. S. Dzhumadil'daev. Generalized Casimir elements. Izvestiya. Mathematics , Tome 27 (1986) no. 2, pp. 391-400. http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a8/

[1] Kostrikin A. I., Shafarevich I. R., “Graduirovannye algebry Li konechnoi kharakteristiki”, Izv. AN SSSR. Seriya matem., 33:2 (1969), 251–322 | MR | Zbl

[2] Ermolaev Yu. B., “Vychislenie tsentralnogo elementa universalnoi obertyvayuschei algebry algebry Vitta”, Izv. Vuzov. Matem., 1975, no. 5, 20–26 | MR | Zbl

[3] Ermolaev Yu. B., “Formula vozvedeniya v stepen proizvedeniya dvukh elementov assotsiativnogo koltsa”, Izv. Vuzov. Matem., 1976, no. 8, 16–27 | MR | Zbl

[4] Ermolaev Yu. B., “O tsentralnykh elementakh universalnoi obertyvayuschei algebry algebry Tsassenkhauza”, Izv. Vuzov. Matem., 1978, no. 6, 73–88 | MR | Zbl

[5] Ermolaev Yu. B., “O strukture tsentra universalnoi obertyvayuschei algebry algebry Tsassenkhauza”, Izv. Vuzov. Matem., 1978, no. 12, 46–59 | MR | Zbl

[6] Ermolaev Yu. B., “Minimalnyi mnogochlen tsentralnogo elementa universalnoi obertyvayuschei algebry algebry Vitta”, Izv. Vuzov. Matem., 1976, no. 10, 32–41 | MR | Zbl

[7] Yakovlev N. I., “Tsentr universalnoi obertyvayuschei algebry algebry Vitta”, Funkts. analiz i ego prilozh., 6:2 (1972), 99–100 | Zbl

[8] Dzhumadildaev A. S., “Neprivodimye predstavleniya silno razreshimykh algebr Li nad polem polozhitelnoi kharakteristiki”, Matem. sb., 123(165):2 (1984), 212–229 | MR

[9] Zassenhaus H., “The representations of Lie algebras of prime characteristic”, Proc. Glasgow Math. Assoc., 2 (1954), 1–36 | DOI | MR | Zbl

[10] Berkson A. J., “The $u$-algebra of a restricted Lie algebria is Frobenius”, Proc. Amer. Math. Soc., 15:1 (1964), 14–15 | DOI | MR | Zbl

[11] Schue J. R., “Symmetry for the enveloping algebra of a restricted Lie algebra”, Proc. Amer. Math. Soc., 16 (1965), 1123–1124 | DOI | MR | Zbl

[12] Block R., “New simple Lie algebras of prime characteristic”, Trans. Amer. Math. Sos., 89:2 (1958), 421–449 | DOI | MR

[13] Ermolaev Yu. B., “Ob odnom klasse algebr Li nad polem prostoi kharakteristiki”, Izv. Vuzov. Matem., 1981, no. 8, 66–70 | MR | Zbl

[14] Ermolaev Yu. B., “Monogennye graduirovannye algebry Li ($q=1$, $r=r_0-1$)”, Izv. Vuzov. Matem., 1981, no. 8, 70–74 | MR | Zbl

[15] Krylyuk Ya. S., “O maksimalnoi razmernosti neprivodimykh predstavlenii prostykh $p$-algebr Li kartanovskikh serii $S$ i $H$”, Matem. sb., 123(165):1 (1984), 108–119 | MR | Zbl