Finite gradings of special linear Lie algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 163-187.

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

In this paper, we study gradings of simple classical Lie algebras with arbitrary Abelian groups and the interconnection of such gradings and automorphism groups of Lie algebras. We give the complete classification of gradings of special linear Lie algebras that are specified by inner automorphisms in the case of an algebraically closed field of zero characteristic.
@article{FPM_2010_16_8_a8,
     author = {A. A. Zolotykh and P. A. Zolotykh},
     title = {Finite gradings of special linear {Lie} algebras},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {163--187},
     publisher = {mathdoc},
     volume = {16},
     number = {8},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a8/}
}
TY  - JOUR
AU  - A. A. Zolotykh
AU  - P. A. Zolotykh
TI  - Finite gradings of special linear Lie algebras
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2010
SP  - 163
EP  - 187
VL  - 16
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a8/
LA  - ru
ID  - FPM_2010_16_8_a8
ER  - 
%0 Journal Article
%A A. A. Zolotykh
%A P. A. Zolotykh
%T Finite gradings of special linear Lie algebras
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2010
%P 163-187
%V 16
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a8/
%G ru
%F FPM_2010_16_8_a8
A. A. Zolotykh; P. A. Zolotykh. Finite gradings of special linear Lie algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 163-187. http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a8/

[1] Burbaki N., Gruppy i algebry Li. Podalgebry Kartana, regulyarnye elementy, rasscheplyaemye poluprostye algebry Li, Mir, M., 1978 | MR

[2] Zhmud E. M., “Ob izomorfnykh neprivodimykh proektivnykh predstavleniyakh konechnykh grupp”, Zapiski mat. otd. fiz.-mat. f-ta KhGU i Khark. mat. ob-va, 26, 1960, 333–372

[3] Zhmud E. M., “Simplekticheskie geometrii na konechnykh abelevykh gruppakh”, Mat. sb., 86(128):1(9) (1971), 9–33 | MR | Zbl

[4] Zhmud E. M., “Simplekticheskie geometrii i proektivnye predstavleniya konechnykh abelevykh grupp”, Mat. sb., 87(129):1 (1972), 3–17 | MR | Zbl

[5] Zolotykh A. A., “Kommutatsionnye faktory i mnogoobraziya assotsiativnykh algebr”, Fundament. i prikl. mat., 3:2 (1997), 453–468 | MR | Zbl

[6] Zolotykh A. A., “Klassifikatsiya proektivnykh predstavlenii konechnykh abelevykh grupp”, Vestn. Mosk. un-ta. Ser. 1. Matematika, mekhanika, 2002, no. 3, 3–10 | MR | Zbl

[7] Kats V. G., “Avtomorfizmy konechnogo poryadka poluprostykh algebr Li”, Funkts. analiz i ego pril., 3:3 (1969), 94–96 | MR | Zbl

[8] Serr Zh.-P., Algebry Li i gruppy Li, Mir, M., 1969 | MR | Zbl

[9] Bahturin Y., Zaicev M., “Gradings on simple Lie algebras of type ‘A’ ”, J. Lie Theory, 16:4 (2006), 719–742 | MR | Zbl

[10] Havlïček M., Patera J., Pelantová E., “On Lie gradings. II”, Linear Algebra Appl., 277:1–3 (1998), 97–125 | MR | Zbl

[11] Scheunert M., “Generalized Lie algebras”, J. Math. Phys., 20 (1979), 712–720 | DOI | MR | Zbl