Solvable Lie algebras with triangular nilradicals
نویسنده
چکیده
All finite-dimensional indecomposable solvable Lie algebras L(n, f), having the triangular algebra T (n) as their nilradical, are constructed. The number of nonnilpotent elements f in L(n, f) satisfies 1 ≤ f ≤ n− 1 and the dimension of the Lie algebra is dim L(n, f) = f + 1 2 n(n − 1).
منابع مشابه
Invariants of Solvable Lie Algebras with Triangular Nilradicals and Diagonal Nilindependent Elements
The invariants of solvable Lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustively. Bases of the invariant sets of all such algebras are constructed by an original purely algebraic algorithm based on Cartan’s method of moving frames.
متن کاملOn the invariants of some solvable rigid Lie algebras
We determine fundamental systems of invariants for complex solvable rigid Lie algebras having nonsplit nilradicals of characteristic sequence (3, 1, .., 1), these algebras being the natural followers of solvable algebras having Heisenberg nilradicals. A special case of this allows us to obtain a criterion to determine the number of functionally independent invariants of rank one subalgebras of ...
متن کاملar X iv : m at h / 06 12 11 7 v 1 [ m at h . D G ] 5 D ec 2 00 6 Nilradicals of Einstein solvmanifolds
A Riemannian Einstein solvmanifold is called standard, if the orthogonal complement to the nilradical of its Lie algebra is abelian. No examples of nonstandard solvmanifolds are known. We show that the standardness of an Einstein metric solvable Lie algebra is completely detected by its nilradical and prove that many classes of nilpotent Lie algebras (Einstein nilradicals, algebras with less th...
متن کاملSolvable Lie algebras with $N(R_n,m,r)$ nilradical
In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.
متن کاملEinstein Solvmanifolds and the Pre-einstein Derivation
An Einstein nilradical is a nilpotent Lie algebra, which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous Einstein spaces) can be reduced to determining, which nilpotent Lie algebras are Einstein nilradicals and to finding, for every Einstein nilradical, its Einstein metric solvable ...
متن کامل