Geodesic
Algebras satisfying Capelli identities
Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 359-370 
K. A. Zubrilin. Algebras satisfying Capelli identities. Sbornik. Mathematics, Tome 186 (1995) no. 3, pp. 359-370. http://geodesic.mathdoc.fr/item/SM_1995_186_3_a3/
@article{SM_1995_186_3_a3,
     author = {K. A. Zubrilin},
     title = {Algebras satisfying {Capelli} identities},
     journal = {Sbornik. Mathematics},
     pages = {359--370},
     year = {1995},
     volume = {186},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_3_a3/}
}
TY  - JOUR
AU  - K. A. Zubrilin
TI  - Algebras satisfying Capelli identities
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 359
EP  - 370
VL  - 186
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_1995_186_3_a3/
LA  - en
ID  - SM_1995_186_3_a3
ER  - 
%0 Journal Article
%A K. A. Zubrilin
%T Algebras satisfying Capelli identities
%J Sbornik. Mathematics
%D 1995
%P 359-370
%V 186
%N 3
%U http://geodesic.mathdoc.fr/item/SM_1995_186_3_a3/
%G en
%F SM_1995_186_3_a3

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

Results on the structure of algebras of any finite signature satisfying Capelli identities over fields and Noetherian commutative associative rings are obtained. It is proved that a finitely generated algebra satisfying Capelli identities of some order has a largest solvable ideal. If, in addition, the algebra is semiprime, then it has only finitely many minimal prime ideals. An estimate is given for the nilpotency class of an ideal that is an obstacle to the representability of a finitely generated algebra satisfying Capelli identities.

[1] Razmyslov Yu. P., “O radikale Dzhekobsona v $\operatorname {PI}$-algebrakh”, Algebra i logika, 13:3 (1974), 337–360 | MR | Zbl

[2] Kemer A. R., “Tozhdestva Kapelli i nilpotentnost radikala konechno porozhdennoi $\operatorname {PI}$-algebry”, DAN SSSR, 245:4 (1980), 793–797 | MR

[3] Lvov I. V., Teorema Brauna o radikale konechno porozhdennoi $\operatorname {PI}$-algebry, Preprint No 63, Institut matematiki SO AN SSSR, Novosibirsk, 1984

[4] Braun A., “The radical in a finitely generated P.I. algebra”, Bull. Amer. Math. Soc., 7:2 (1982), 385–386 | DOI | MR | Zbl

[5] Razmyslov Yu. P., “Algebry, udovletvoryayuschie tozhdestvennym sootnosheniyam tipa Kapelli”, Izv. AN SSSR. Ser. matem., 45:1 (1981), 143–166 | MR | Zbl

[6] Mischenko S. P., “Variant teoremy o vysote dlya algebr Li”, Matem. zametki, 47:4 (1990), 83–89 | MR

[7] Razmyslov Yu. P., Tozhdestva algebr i ikh predstavlenii, Nauka, M., 1989 | MR | Zbl