Invariants of Solvable Lie Algebras with Triangular Nilradicals and Diagonal Nilindependent Elements
نویسندگان
چکیده
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.
منابع مشابه
Invariants of Triangular Lie Algebras with One Nilindependent Diagonal Element
The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are constructed using an original algebraic algorithm based on Cartan’s method of moving frames. The conjecture of Tremblay and Winternitz [J.Phys. A: Math. Gen., 2001, V.34, 9085] on the number and form of elements in the bases i...
متن کاملInvariants of the nilpotent and solvable triangular Lie algebras
Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras T (M), isomorphic to the algebras of upper triangular M × M matrices. The Lie algebra T (M) is shown to have [M/2] functionally independent invariants. They can all be chosen to be polynomials and they are presented explicitly. The second class consist...
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 کاملSolvable Lie algebras with triangular nilradicals
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).
متن کاملInvariants of Lie Algebras with Fixed Structure of Nilradicals
An algebraic algorithm is developed for computation of invariants (‘generalized Casimir operators’) of general Lie algebras over the real or complex number field. Its main tools are the Cartan’s method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. Unlike the first application of the algorithm in [J.Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602...
متن کامل