117
Views
6
CrossRef citations to date
0
Altmetric
Articles

Itô’s theorem and metabelian Leibniz algebras

&
Pages 2187-2199 | Received 25 Jul 2014, Accepted 24 Nov 2014, Published online: 24 Dec 2014

References

  • Amberg B, Franciosi S, de Giovanni F. Products of groups. New York (NY): Oxford University Press; 1992.
  • Itô N. Über das produkt von zwei abelschen gruppen [About the product of two abelian groups]. Math. Z. 1955;62:400–401.
  • Conder MDE, Isaacs IM. Derived subgroups of products of an abelian and a cyclic subgroup. J. London Math. Soc. 2004;69:333-348.
  • Bahturin Yu, Kegel OH. Universal sums of abelian subalgebras. Comm. Algebra. 1995;23:2975–2990.
  • Burde D. Derived length and nildecomposable Lie algebras. arXiv:1212.3113.
  • Petravchuk AP. On the sum of an almost abelian Lie algebra and a Lie algebra finite dimensional over its center. Ukrain. Math. J. 1999;51:707–715.
  • Chen Yongshan, Chen Yuqun. Gröbner–Shirshov bases for metabelian Lie algebras. J. Algebra. 2012;358:143–161.
  • Dangovski R, Drensky V, Findik Ş. Weitzenböck derivations of free metabelian Lie algebras. Linear Algebra Appl. 2013;439:3279–3296.
  • Daniyarova E, Kazachkov I, Remeslennikov V. Algebraic geometry over free metabelian Lie algebra II: finite field case. J. Math. Sci. 2006;135:3311–3326.
  • Drensky V, Piacentini Cattaneo GM. Varieties of metabelian Leibniz algebras. J. Algebra Appl. 2002;01:31–50.
  • Poroshenko EN, Timoshenko EI. Universal equivalence of partially commutative metabelian Lie algebras. J. Algebra. 2013;384:143–168.
  • Agore AL, Militaru G. Unified products for Leibniz algebras applications. Linear Algebra Appl. 2013;439:2609–2633.
  • Calderon Martin AJ, Sanchez Delgado JM. On split Leibniz algebras. Linear Algebra Appl. 2012;436:1651–1663.
  • Camacho LM, Cañetea EM, Gómez JR, Redjepov ShB. Leibniz algebras of nilindex n − 3 with characteristic sequence (n − 3, 2, 1). Linear Algebra Appl. 2013;438:1832–1851.
  • Cañetea EM, Khudoyberdiyev AKh. The classification of 4-dimensional Leibniz algebras. Linear Algebra Appl. 2013;439:273–288.
  • Casas JM, Ladra M, Omirov BA, Karimjanov IA. Classification of solvable Leibniz algebras with null-filiform nilradical. Linear Multilinear Algebra. 2013;61:758–774.
  • Covez S. The local integration of Leibniz algebras. Ann. Inst. Fourier. 2013;63:1–35.
  • Cuvier C. Algèbres de Leibniz: définitions, propriétés [Leibniz algebras: definitions, properties]. Ann. Scient. Ec. Norm. Sup. 1994;27:1–45.
  • Demir I, Misra KC, Stitzinger E. On some structures of Leibniz algebras. arXiv:1307.7672.
  • Fialowski A, Khudoyberdiyev AKh, Omirov BA. A characterization of nilpotent Leibniz algebras. Algebr. Represent. Theor. 2013;16:1489–1505.
  • Loday J-L, Pirashvili T. Universal enveloping algebras of Leibniz algebras and (co)homology. Math. Ann. 1993;296:139–158.
  • Omirov BA, Rakhimov IS, Turdibaev RM. On description of Leibniz algebras corresponding to 𝔰𝔩2. Algebr. Represent. Theor. 2013;16:1507–1519.
  • Burde D, Ceballos M. Abelian ideals of maximal dimension for solvable Lie algebras. J. Lie Theory. 2012;22:741–756.
  • Ceballos M, Towers DA. On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras. J. Pure Appl. Algebra. 2014;218:497–503.
  • de Graaf WA. Classification of solvable Lie algebras. Exp. Math. 2005;14:15–25.
  • Turkowski P. Solvable Lie algebras of dimension six. J. Math. Phys. 1990;31:1344–1350.
  • Szechtman F. Equivalence and normal forms of bilinear forms. Linear Algebra Appl. 2014;443:245–259.
  • Gauger M. On the classification of metabelian Lie algebras. Trans. Amer. Math. Soc. 1973;179:293–329.
  • Galitski LYu, Timashev DA. On classification of metabelian Lie algebras. J. Lie Theory. 1999;9:125–156.
  • del Barcoa VJ, Ovandob GP. Free nilpotent Lie algebras admitting ad-invariant metrics. J. Algebra. 2012;366:205–216.
  • Agaoka Y. An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras. Linear Algebra Appl. 2002;345:85–118.
  • Militaru G. The global extension problem, co-flag and metabelian Leibniz algebras. Linear Multilinear Algebra, 2015;63:601–621.
  • Agore AL, Militaru G. Extending structures for Lie algebras. Monatsh. Math. 2014;174:169–193.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.