Related papers: Invariants of Triangular Lie Algebras
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…
A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie…
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 $M\times M$ matrices. The Lie algebra…
A purely algebraic algorithm for computation of invariants (generalized Casimir operators) of Lie algebras by means of moving frames is discussed. Results on the application of the method to computation of invariants of low-dimensional Lie…
We finish the determination of the invariants of the coadjoint representation of six dimensional real Lie algebras, by determining a fundamental set of invariants for the 99 isomorphism classes of solvable Lie algebras with five dimensional…
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…
Casimir invariants for quantized affine Lie algebras are constructed and their eigenvalues computed in any irreducible highest weight representation.
We consider the Casimir Invariants related to some a special kind of Lie-algebra extensions, called universal extensions. We show that these invariants can be studied using the equivalence between the universal extensions and the…
The Casimir operators of a Lie algebra are in one-to-one correspondence with the symmetric invariant tensors of the algebra. There is an infinite family of Casimir operators whose members are expressible in terms of a number of primitive…
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…
The generalized Casimir invariants of real indecomposable Lie algebras admitting a nontrivial Levi decomposition are determined.
We use computer algebra to determine the Lie invariants of degree <= 12 in the free Lie algebra on two generators corresponding to the natural representation of the simple 3-dimensional Lie algebra sl(2,C). We then consider the free Lie…
The coefficient algebra of a finite-dimensional Lie algebra on a finite-dimensional representation is defined as the subalgebra generated by all coefficients of the corresponding characteristic polynomial. We explore connections between…
A quadratic Lie algebra is a Lie algebra endowed with a symmetric, invariant and non degenerate bilinear form; such a bilinear form is called an invariant metric. The aim of this work is to describe the general structure of those central…
The indecomposable solvable Lie algebras with graded nilradical of maximal nilindex and a Heisenberg subalgebra of codimension one are analyzed, and their generalized Casimir invariants calculated. It is shown that rank one solvable…
We introduce the concept of a triangular representation of a Lie algebra, give a counterpart of Ado's theorem, and discuss $2$-irreducible triangular modules over a nonreductive Lie algebra.
We show that any semi-direct sum $L$ of Lie algebras with Levi factor $S$ must be perfect if the representation associated with it does not possess a copy of the trivial representation. As a consequence, all invariant functions of $L$ must…
We introduce invariant algebras and representation$^{(c_1,..., c_8)}$ of algebras, and give many ways of constructing Lie algebras, Jordan algebras, Leibniz algebras, pre-Lie algebras and left-symmetric algebras in an invariant algebras.
The invariants of all complex solvable rigid Lie algebras up to dimension eight are computed. Moreover we show, for rank one solvable algebras, some criteria to deduce to non-existence of non-trivial invariants or the existence of…
We investigate the group gradings on the algebra of upper triangular matrices over an arbitrary field, viewed as a Lie algebra. These results were obtained a few years early by the same authors. We provide streamlined proofs, and present a…