FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS

Yıl 2019, , 64 - 76, 08.01.2019

Allison Mcalister Kristen Stagg Rovira Ernie Stitzinger

https://doi.org/10.24330/ieja.504114

Cited By: 1

Öz

Ideals that share properties with the Frattini ideal of a Leibniz

algebra are studied. Similar investigations have been considered in group the-

ory. The results will hold for Lie algebras as well. Many of the results involve

nilpotency of these algebras.

Anahtar Kelimeler

Frattini ideal, Cartan subalgebra, primitive ideal, non-generator

Kaynakça

• Sh. A. Ayupov and B. A. Omirov, On Leibniz algebras, Algebra and operator theory (Tashkent, 1997), Kluwer Acad. Publ., Dordrecht, (1998), 1-12.
• D. W. Barnes, Some theorems on Leibniz algebras, Comm. Algebra, 39(7) (2011), 2463-2472.
• D. W. Barnes, Schunck classes of soluble Leibniz algebras, Comm. Algebra, 41(11) (2013), 4046-4065.
• C. Batten, L. Bosko-Dunbar, A. Hedges, J. T. Hird, K. Stagg and E. Stitzinger, A Frattini Theory for Leibniz algebras, Comm. Algebra, 41(4) (2013), 1547- 1557.
• C. Batten Ray, A. Combs, N. Gin, A. Hedges, J. T. Hird and L. Zack, Nilpotent Lie and Leibniz algebras, Comm. Algebra, 42(6) (2014), 2404-2410.
• C. Batten Ray, A. Hedges and E. Stitzinger, Classifying several classes of Leibniz algebras, Algebr. Represent. Theory, 17(2) (2014), 703-712.
• J. C. Beidleman and T. K. Seo, Generalized Frattini subgroups of nite groups, Pacic J. Math., 23 (1967), 441-450.
• L. Bosko, A. Hedges, J. T. Hird, N. Schwartz and K. Stagg, Jacobson's rene- ment of Engel's theorem for Leibniz algebras, Involve, 4(3) (2011), 293-296.
• T. Burch, M. Harris, A. McAlister, E. Rogers, E. Stitzinger and S. M. Sullivan, 2-recognizeable classes of Leibniz algebras, J. Algebra, 423 (2015), 506-513.
• I. Demir, K. Misra and E. Stitzinger, On some structures of Leibniz algebras, Recent advances in representation theory, quantum groups, algebraic geometry, and related topics, Amer. Math. Soc., Providence, RI, Contemp. Math., 623 (2014), 41-54.
• L.-C. Kappe and J. Kirkland, Some analogues of the Frattini subgroup, Algebra Colloq., 4(4) (1997), 419-426.
• J.-L. Loday, Une version non commutative des algebres de Lie: les algebres de Leibniz, Enseign. Math., 39 (1993), 269-293.
• K. Stagg, Analogues of the Frattini subalgebra, Int. Electron. J. Algebra, 9 (2011), 124-132.
• D. A. Towers, A Frattini theory for algebras, Proc. London Math. Soc., 27 (1973), 440-462.
• D. Towers, Two ideals of an algebra closely related to its Frattini ideal, Arch. Math. (Basel), 35(1-2) (1980), 112-120.