On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras
نویسندگان
چکیده
منابع مشابه
Abelian Ideals of Maximal Dimension for Solvable Lie Algebras
We compare the maximal dimension of abelian subalgebras and the maximal dimension of abelian ideals for finite-dimensional Lie algebras. We show that these dimensions coincide for solvable Lie algebras over an algebraically closed field of characteristic zero. We compute this invariant for all complex nilpotent Lie algebras of dimension n ≤ 7. Furthermore we study the case where there exists an...
متن کاملAlgorithmic method to obtain abelian subalgebras and ideals in Lie algebras
Algorithmic method to obtain abelian subalgebras and ideals in Lie algebras Manuel Ceballos a , Juan Núñez a & Ángel F. Tenorio b a Departamento de Geometría y Topología, Facultad de Matemáticas., Universidad de Sevilla, Aptdo. 1160, 41080, Seville, Spain b Departamento de Economía, Métodos Cuantitativos e Historia Económica, Escuela Politécnica Superior, Universidad Pablo de Olavide, Ctra. Utr...
متن کاملAbelian Ideals with given Dimension in Borel Subalgebras
A well-known Peterson’s theorem says that the number of abelian ideals in a Borel subalgebra of a rank-r finite dimensional simple Lie algebra is exactly 2r . In this paper, we determine the dimensional distribution of abelian ideals in a Borel subalgebra of finite dimensional simple Lie algebras, which is a refinement of the Peterson’s theorem capturing more Lie algebra invariants.
متن کاملSolvable Lie Algebras and Maximal Abelian Dimensions
In this paper some results on the structure of finite-dimensional Lie algebras are obtained by means of the concept of maximal abelian dimension. More concretely, a sufficient condition is given for the solvability in finite-dimensional Lie algebras by using maximal abelian dimensions. Besides, a necessary condition for the nilpotency is also stated for such Lie algebras. Finally, the maximal a...
متن کاملComputational Algorithm for Obtaining Abelian Subalgebras in Lie Algebras
The set of all abelian subalgebras is computationally obtained for any given finite-dimensional Lie algebra, starting from the nonzero brackets in its law. More concretely, an algorithm is described and implemented to compute a basis for each nontrivial abelian subalgebra with the help of the symbolic computation package MAPLE. Finally, it is also shown a brief computational study for this impl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2014
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2013.06.017