For the inhomogeneous pseudo-unitary Lie algebras Iu(p, q) a determinantal method to compute the Casimir operators is given, independently of the traditional analysis of the enveloping algebra. This procedure is extended to contractions of Iu(p, q) isomorphic to an extension by a derivation of the inhomogeneous special pseudo-unitary Lie algebras Isu(p − 1, q), providing an alternative analytic...

In this paper we explicitly determine the derivation algebra, automorphism group of quasi Qn-filiform Lie algebras, and applying some properties of root vector decomposition we obtain their isomorphism theorem. AMS Classification: 17B05; 17B30

Let $\mathbb C_Q$ denote a rational quantum torus with $d$ variables, and $\mathcal Z$ be the centre of C_Q$. In this paper we give explicit description structure cuspidal modules for derivation Lie algebra D$ over C_Q$, an extra associative Z$-action.

We present a systematic derivation for a general formula for the n-point coupling constant valid for affine Toda theories related to any simple Lie algebra g. All n-point couplings with n ≥ 4 are completely determined in terms of the masses and the three-point couplings. A general fusing rule, formulated in the root space of the Lie algebra, is derived for all n-point couplings.

A vector eld on a connected Lie group is said to be linear if its ow is a one parameter group of automorphisms. A control-a ne system is linear if the drift is linear and the controlled vector elds right invariant. The controllability properties of such systems are studied, mainly in the case where the derivation of the group Lie algebra that can be associated to the linear vector eld is inner....

W. H. Davenport has shown that the derivation algebra 3)(4) of a semisimple Malcev algebra A of characteristic 0 acts completely reducibly on A. The purpose of the present note is to characterize those Malcev algebras which have such derivation algebras as those whose radical is central and to obtain the same result for Lie triple systems. Analogous results are known to hold for standard and al...

Let M be a 2 and 3-torsion free prime Γ-ring, d a nonzero derivation on M and U a nonzero Lie ideal of M . In this paper it is proved that U is a central Lie ideal of M if d satisfies one of the following (i) d(U) ⊂ Z, (ii) d(U) ⊂ U and d(U) = 0, (iii) d(U) ⊂ U , d(U) ⊂ Z.

A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the difference equation. The renormalization group equation is a Lie differential equation of a Lie group which leaves the system approximately invariant. For a 2-D ...

In one of our recent papers, the associative and the Lie algebras of Weyl type A[D] = A⊗IF [D] were defined and studied, where A is a commutative associative algebra with an identity element over a field IF of any characteristic, and IF [D] is the polynomial algebra of a commutative derivation subalgebra D of A. In the present paper, a class of the above associative and Lie algebras A[D] with I...

In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we deduce an intrinsic framework for this type of dynamical systems. Interesting applications as, for instance, a geometric derivation of the higher-order Euler-Po...