On minimal non-elementary Lie algebras
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- by David A. Towers
- Proc. Amer. Math. Soc. 143 (2015), 117-120
- DOI: https://doi.org/10.1090/S0002-9939-2014-12224-6
- Published electronically: August 29, 2014
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Abstract:
The class of minimal non-elementary Lie algebras over a field $F$ are studied. These are classified when $F$ is algebraically closed and of characteristic different from $2,3$. The solvable algebras in this class are also characterised over any perfect field.References
- Alberto Elduque, A note on the Frattini subalgebra of a nonassociative algebra, Nonassociative algebraic models (Zaragoza, 1989) Nova Sci. Publ., Commack, NY, 1992, pp. 119–129. MR 1189616
- A. A. Premet and K. N. Semenov, Varieties of residually finite Lie algebras, Mat. Sb. (N.S.) 137(179) (1988), no. 1, 103–113, 144 (Russian); English transl., Math. USSR-Sb. 65 (1990), no. 1, 109–118. MR 965882, DOI 10.1070/SM1990v065n01ABEH001142
- Kristen Stagg and Ernest Stitzinger, Minimal non-elementary Lie algebras, Proc. Amer. Math. Soc. 139 (2011), no. 7, 2435–2437. MR 2784809, DOI 10.1090/S0002-9939-2010-10711-6
- D. A. Towers, A Frattini theory for algebras, Proc. London Math. Soc. (3) 27 (1973), 440–462. MR 427393, DOI 10.1112/plms/s3-27.3.440
- D. A. Towers, Elementary Lie algebras, J. London Math. Soc. (2) 7 (1973), 295–302. MR 376782, DOI 10.1112/jlms/s2-7.2.295
- David A. Towers and Vicente R. Varea, Elementary Lie algebras and Lie $A$-algebras, J. Algebra 312 (2007), no. 2, 891–901. MR 2333190, DOI 10.1016/j.jalgebra.2006.11.034
- David A. Towers and Vicente R. Varea, Further results on elementary Lie algebras and Lie $A$-algebras, Comm. Algebra 41 (2013), no. 4, 1432–1441. MR 3044418, DOI 10.1080/00927872.2011.643667
Bibliographic Information
- David A. Towers
- Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England
- MR Author ID: 173875
- Email: d.towers@lancaster.ac.uk
- Received by editor(s): February 5, 2013
- Received by editor(s) in revised form: April 1, 2013
- Published electronically: August 29, 2014
- Communicated by: Kailash C. Misra
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 143 (2015), 117-120
- MSC (2010): Primary 17B05, 17B20, 17B30, 17B50
- DOI: https://doi.org/10.1090/S0002-9939-2014-12224-6
- MathSciNet review: 3272736