Yıl 2017, Cilt 21, Sayı 21, Sayfalar 55 - 75 2017-01-17

DERIVATIONS OF TERNARY LIE ALGEBRAS AND GENERALIZATIONS

Amine Ben Abdeljelil [1] , Mohamed Elhamdadi [2] , Abdenacer Makhlouf [3]

175 149

We study derivations of ternary Lie algebras. Precisely, we investigate the relation between derivations of Lie algebras and the induced ternary Lie algebras. We also explore the spaces of quasi-derivations, the centroid and the quasi-centroid and give some properties. Finally, we compute these spaces for low dimensional ternary Lie algebras g. 

Ternary Lie algebra, ternary Lie algebra induced by Lie algebra
  • [1] J. Arnlind, A. Kitouni, A. Makhlouf and S. Silvestrov, Structure and cohomology
  • of 3-Lie algebras induced by Lie algebras, Algebra, geometry and mathematical
  • physics, 123-144, Springer Proc. Math. Stat., 85, Springer, Heidelberg, 2014.
  • [2] J. Arnlind, A.Makhlouf and S. Silvestrov, Ternary Hom-Nambu-Lie algebras
  • induced by Hom-Lie algebras, J. Math. Phys., 51(4) (2010), 043515, 11 pp.
  • [3] J. Arnlind, A. Makhlouf and S. Silvestrov, Construction of n-Lie algebras and
  • n-ary Hom-Nambu-Lie algebras, J. Math. Phys., 52(12) (2011), 123502, 13 pp.
  • [4] R. Bai, J. Wang and Z. Li, Derivations of the 3-Lie algebra realized by gl(n, C),
  • J. Nonlinear Math. Phys., 18(1) (2011), 151-160.
  • [5] V. T. Filippov, n-Lie algebras, Sibirsk. Mat. Zh., 26(6) (1985), 126-140.
  • [6] V. T. Filippov, On δ-derivations of Lie algebras, (Russian) Sibirsk. Mat. Zh.,
  • 39(6) (1998), 1409-1422, iv; translation in Siberian Math. J. 39(6) (1998), 1218-1230.
  • [7] M. E. Gordji, R. Farrokhzad and S. A. Hosseinioun, Ternary (σ, τ, ξ)-
  • derivations on Banach ternary algebras, Int. J. Nonlinear Anal. Appl., 5(1)(2014), 23-35.
  • [8] M. R. Hestenes, A ternary algebra with applications to matrices and linear
  • transformations, Arch. Rational Mech. Anal., 11 (1962), 138-194.
  • [9] I. Kaygorodov, On δ-derivations of n-ary algebras, (Russian) Izv. Ross. Akad.
  • Nauk Ser. Mat., 76(6) (2012), 81-94; translation in Izv. Math., 76(6) (2012),1150-1162.
  • [10] I. Kaygorodov and Y. Popov, Generalized derivations of (color) n-ary algebras,
  • Linear Multilinear Algebra, 64(6) (2016), 1086-1106.
  • [11] G. F. Leger and E. M. Luks, Generalized derivations of Lie algebras, J. Algebra,
  • 228(1) (2000), 165-203.
  • [12] W. G. Lister, A structure theory of Lie triple systems, Trans. Amer. Math.
  • Soc., 72 (1952), 217-242.
  • [13] P. Novotný and J. Hrivnák, On (α, β, γ)-derivations of Lie algebras and corresponding
  • invariant functions, J. Geom. Phys., 58(2) (2008), 208-217.
  • [14] J. M. Perez-Izquierdo, Unital algebras, ternary derivations, and local triality,
  • Algebras, representations and applications, Contemp. Math., 483, Amer.
  • Math. Soc., Providence, RI, (2009), 205-220.
  • [15] Y. Sheng, Representations of hom-Lie algebras, Algebr. Represent. Theory,
  • 15(6) (2012), 1081-1098.
Konular Matematik ve İstatistik
Dergi Bölümü Makaleler
Yazarlar

Yazar: Amine Ben Abdeljelil

Yazar: Mohamed Elhamdadi

Yazar: Abdenacer Makhlouf

Bibtex @araştırma makalesi { ieja296030, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {21}, pages = {55 - 75}, doi = {10.24330/ieja.296030}, title = {DERIVATIONS OF TERNARY LIE ALGEBRAS AND GENERALIZATIONS}, key = {cite}, author = {Elhamdadi, Mohamed and Abdeljelil, Amine Ben and Makhlouf, Abdenacer} }
APA Abdeljelil, A , Elhamdadi, M , Makhlouf, A . (2017). DERIVATIONS OF TERNARY LIE ALGEBRAS AND GENERALIZATIONS. International Electronic Journal of Algebra, 21 (21), 55-75. DOI: 10.24330/ieja.296030
MLA Abdeljelil, A , Elhamdadi, M , Makhlouf, A . "DERIVATIONS OF TERNARY LIE ALGEBRAS AND GENERALIZATIONS". International Electronic Journal of Algebra 21 (2017): 55-75 <http://dergipark.gov.tr/ieja/issue/27921/296030>
Chicago Abdeljelil, A , Elhamdadi, M , Makhlouf, A . "DERIVATIONS OF TERNARY LIE ALGEBRAS AND GENERALIZATIONS". International Electronic Journal of Algebra 21 (2017): 55-75
RIS TY - JOUR T1 - DERIVATIONS OF TERNARY LIE ALGEBRAS AND GENERALIZATIONS AU - Amine Ben Abdeljelil , Mohamed Elhamdadi , Abdenacer Makhlouf Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.296030 DO - 10.24330/ieja.296030 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 55 EP - 75 VL - 21 IS - 21 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.296030 UR - http://dx.doi.org/10.24330/ieja.296030 Y2 - 2016 ER -
EndNote %0 International Electronic Journal of Algebra DERIVATIONS OF TERNARY LIE ALGEBRAS AND GENERALIZATIONS %A Amine Ben Abdeljelil , Mohamed Elhamdadi , Abdenacer Makhlouf %T DERIVATIONS OF TERNARY LIE ALGEBRAS AND GENERALIZATIONS %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 21 %N 21 %R doi: 10.24330/ieja.296030 %U 10.24330/ieja.296030
ISNAD Abdeljelil, Amine Ben , Elhamdadi, Mohamed , Makhlouf, Abdenacer . "DERIVATIONS OF TERNARY LIE ALGEBRAS AND GENERALIZATIONS". International Electronic Journal of Algebra 21 / 21 (Ocak 2017): 55-75. http://dx.doi.org/10.24330/ieja.296030