Geodesic
On Equality of Certain Derivations of Lie Algebras
Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 2, pp. 153-164.

Voir la notice de l'article provenant de la source Library of Science

Let L be a Lie algebra. A derivation α of L is a commuting derivation (central derivation), if α (x) ∈ CL (x) (α (x) ∈ Z (L)) for each x ∈ L. We denote the set of all commuting derivations (central derivations) by (L) (Derz (L)). In this paper, first we show (L) is subalgebra from derivation algebra L, also we investigate the conditions on the Lie algebra L where commuting derivation is trivial and finally we introduce the family of nilpotent Lie algebras in which Derz (L) = (L).
Keywords: derivation, central derivation, centralizer, commuting derivation 
@article{DMGAA_2019_39_2_a0,
     author = {Amiri, Azita and Saeedi, Farshid and Alemi, Mohammad Reza},
     title = {On {Equality} of {Certain} {Derivations} of {Lie} {Algebras}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {153--164},
     publisher = {mathdoc},
     volume = {39},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2019_39_2_a0/}
}
TY  - JOUR
AU  - Amiri, Azita
AU  - Saeedi, Farshid
AU  - Alemi, Mohammad Reza
TI  - On Equality of Certain Derivations of Lie Algebras
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2019
SP  - 153
EP  - 164
VL  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2019_39_2_a0/
LA  - en
ID  - DMGAA_2019_39_2_a0
ER  - 
%0 Journal Article
%A Amiri, Azita
%A Saeedi, Farshid
%A Alemi, Mohammad Reza
%T On Equality of Certain Derivations of Lie Algebras
%J Discussiones Mathematicae. General Algebra and Applications
%D 2019
%P 153-164
%V 39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2019_39_2_a0/
%G en
%F DMGAA_2019_39_2_a0
Amiri, Azita; Saeedi, Farshid; Alemi, Mohammad Reza. On Equality of Certain Derivations of Lie Algebras. Discussiones Mathematicae. General Algebra and Applications, Tome 39 (2019) no. 2, pp. 153-164. http://geodesic.mathdoc.fr/item/DMGAA_2019_39_2_a0/

[1] H.E. Bell and W.S. Martindale, Centralizing mappings of semiprime rings, Canad. Math. Bull 30 (1987) 92–101. doi:10.1016/j.laa.2011.06.037

[2] S. Cicalo, W.A. de Graaf and C. Schneider, Six-dimensional nilpotent Lie algebras, Linear Algebra Appl. 436 (2012) 163–189. doi:10.1007/BF02638378

[3] M. Deaconescu, G. Silberberg and G.L. Walls, On commuting automorphisms of groups, Arch. Math. (Basel) 79 (2002) 423–429. doi:10.1006/jabr.2000.8655

[4] M. Deaconescu and G.L. Walls, Right 2 -Engel elements and commuting automorphisms of groups, J. Algebra 238 (2001) 479–484. doi:10.1006/jabr.2000.8655

[5] N. Divinsky, On commuting automorphisms of rings, Trans. Roy. Soc. Canada. Sect. III 49 (1955) 19–22. doi:10.12691/jmsa-2-3-1

[6] S. Fouladi and R. Orfi, Commuting automorphisms of some finite groups, Glas. Mat. Ser. III 48 (2013) 91–96. doi:10.3336/gm.48.1.08

[7] W.A. de Graaf, Classification of 6 -dimensional nilpotent Lie algebras over fields of characteristic not 2, J. Algebra 309 (2007) 640–653. doi:10.1016/j.jalgebra.2006.08.006

[8] I.N. Herstein, Problem proposal, Amer. Math. Monthly 91 (1984), 203.

[9] I.N. Herstein, T.J. La ey and J. Thomas, Problems and solutions: solutions of elementary problems E3039, Amer. Math. Monthly 93 (1986) 816–817. doi:10.2307/2322945

[10] J. Luh, A note on commuting automorphisms of rings, Amer. Math. Monthly 77 (1970) 61–62. doi:10.1080/00029890.1970.11992420

[11] E.I. Marshall, The Frattini subalgebra of a Lie algebra, J. London Math. Soc. 42 (1967) 41–422. doi:10.1112/jlms/s1-42.1.416

[12] M. Pettet, Personal communication.

[13] F. Saeedi and S. Sheikh-Mohseni, A characterization of stem algebras in terms of central derivations, Algebr. Represent. Theory 20 (2017) 1143–1150. doi:10.1007/s10468-017-9680-5

[14] S. Sheikh-Mohseni, F. Saeedi and M. Badrkhani Asl, On special subalgebras of derivations of Lie algebras, Asian-Eur. J. Math. 8 (2015), 1550032. doi:10.1142/S1793557115500321

[15] S. Tôgô, Derivations of Lie algebras, J. Sci. Hiroshima Univ. Ser. A, Series A-I 28 (1964) 133–158. doi:10.32917/hmj/1206139393

[16] F. Vosooghpour, Z. Kargarian and M. Akhavan-Malayeri, Commuting automorphism of p-groups with cyclic maximal subgroups, Commun. Korean Math. Soc. 28 (2013) 643–647. doi:10.1142/S0219498819502086