Location of Repository

C-Ideals of Lie Algebras.

Abstract

A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B \cap C \leq B_L, where B_L is the largest ideal of L contained in B. This is analogous to the concept of c-normal subgroup, which has been studied by a number of authors. We obtain some properties of c-ideals and use them to give some characterisations of solvable and supersolvable Lie algebras. We also classify those Lie algebras in which every one-dimensional subalgebra is a c-ideal

Year: 2009
OAI identifier: oai:eprints.lancs.ac.uk:19877
Provided by: Lancaster E-Prints

Citations

1. (2005). A note on c-normal subgroups of ﬁnite groups.
2. (1973). A.: A Frattini theory for algebras.
3. (1972). Abstract Lie algebras.
4. (1996). C-normality of groups and its properties.
5. (1962). Nilpotency of Lie algebras.
6. (1981). On Lie algebras in which modular pairs of subalgebras are permutable.
7. (1984). On subalgebras of simple Lie algebras of characteristic p
8. (1967). On the cohomology of soluble Lie algebras.
9. (2000). Some conditions for solubility.
10. (1956). Sous-alg ebres de Cartan et d´ ecompositions de Levi dans les alg ebres de Lie (French).
11. (2000). The inﬂuence of c-normality on the structure of ﬁnite groups.
12. (1998). The inﬂuence of minimal subgroups on the structure of ﬁnite groups,
13. (2000). The inﬂuence of minimal subgroups on the structure of ﬁnite groups.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.