Geodesic
Local automorphisms and local derivations of nilpotent matrix algebras
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 9-19
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study general properties and ties of local automorphisms and local derivations of nilpotent algebras. Also we construct examples of nontrivial local automorphisms and local derivations of algebra of niltriangular $n\times n$ matrixes (they are completely described in case $n=3$) and corresponding subalgebra in the Chevalley algebras.
Keywords: nilpotent algebra; niltriangular matrix; Chevalley algebra; local derivations; local automorphisms. 
@article{IIGUM_2011_4_1_a1,
     author = {A. P. Elisova and I. N. Zotov and V. M. Levchuk and G. S. Suleimanova},
     title = {Local automorphisms and local derivations of nilpotent matrix algebras},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {9--19},
     year = {2011},
     volume = {4},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a1/}
}
TY  - JOUR
AU  - A. P. Elisova
AU  - I. N. Zotov
AU  - V. M. Levchuk
AU  - G. S. Suleimanova
TI  - Local automorphisms and local derivations of nilpotent matrix algebras
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2011
SP  - 9
EP  - 19
VL  - 4
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a1/
LA  - ru
ID  - IIGUM_2011_4_1_a1
ER  - 
%0 Journal Article
%A A. P. Elisova
%A I. N. Zotov
%A V. M. Levchuk
%A G. S. Suleimanova
%T Local automorphisms and local derivations of nilpotent matrix algebras
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2011
%P 9-19
%V 4
%N 1
%U http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a1/
%G ru
%F IIGUM_2011_4_1_a1
A. P. Elisova; I. N. Zotov; V. M. Levchuk; G. S. Suleimanova. Local automorphisms and local derivations of nilpotent matrix algebras. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 1, pp. 9-19. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_1_a1/

[1] A. P. Elisova, “Lokalnye avtomorfizmy algebry niltreugolnykh matrits nad koltsom”, Algebra, logika i metodika obucheniya matematiki, Materialy Vseros. konf., KGPU, Krasnoyarsk, 2010, 37–42

[2] I. N. Zotov, “Lokalnye avtomorfizmy nilpotentnykh algebr matrits malykh stepenei”, Tr. XLII kraevoi nauch. stud. konf. po matematike i kompyuternym naukam (Sib. feder. un-t), IPK SFU, Krasnoyarsk, 2009, 24–25

[3] A. G. Kurosh, Lektsii po obschei algebre, Nauka, M., 1973

[4] V. M. Levchuk, “Avtomorfizmy unipotentnykh podgrupp grupp lieva tipa”, Algebra i logika, 29 (1990), 141–161 | MR | Zbl

[5] V. M. Levchuk, “Svyazi unitreugolnoi gruppy s nekotorymi koltsami. II: Gruppy avtomorfizmov”, Sib. mat. zhurn., 24:4 (1983), 543–557 | MR | Zbl

[6] V. M. Levchuk, E. V. Minakova, “Elementarnaya ekvivalentnost i izomorfizmy lokalno-nilpotentnykh matrichnykh grupp i kolets”, DAN, 425:2 (2009), 165–168 | MR | Zbl

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

[8] R. Carter, Simple groups of Lie type, Wiley and Sons, N.Y., 1972 | MR | Zbl

[9] R. Crist, “Local automorphisms”, Proc. Amer. Math. Soc., 128 (2000), 1409–1414 | DOI | MR | Zbl

[10] M. Ghosseiri, N. Nader, “Jordan derivations of some classes of matrix rings”, Taiwanese J. Math., 11 (2007), 51–62 | MR | Zbl

[11] D. Hadwin, J. Li, “Local derivations and local automorphisms”, J. Math. Analysis and Applications, 290 (2004), 702–714 | DOI | MR | Zbl

[12] R. Kadison, “Local derivations”, J. Algebra, 130 (1990), 494–509 | DOI | MR | Zbl

[13] D. R. Larson, A. R. Sourour, “Local derivations and local automorphisms of $B(H)$”, Proc. Sympos. Pure Math., 51 (1990), 187–194 | DOI | MR | Zbl

[14] V. M. Levchuk, O. V. Radchenko, “Derivations of the locally nilpotent matrix rings”, J. Algebra and Applications, 9:5 (2010), 717–724 | DOI | MR | Zbl