On filtered manifolds one can define a different notion of order for the differential operators. In this paper, we use generalized fixed point algebras to construct pseudodifferential extension that reflects behaviour. corresponding calculus, principal symbol an operator is family operators acting on certain nilpotent Lie groups. The role ellipticity as Fredholm condition replaced by Rockland t...

In this paper we study the Green function for a second order noncoercive differential operator L on a connected, simply connected homogeneous manifold of negative curvature. Such a manifold is a solvable Lie group S = NA, a semi-direct product of a nilpotent Lie group N and an abelian group A = R. Moreover, for an H belonging to the Lie algebra a of A, the real parts of the eigenvalues of Adexp...

In this paper we study the Lie algebras of derivations two-step nilpotent algebras. We obtain a class with trivial center and abelian ideal inner derivations. Among these, relations between complex real case indecomposable Heisenberg Leibniz are thoroughly described. Finally show that every almost derivation algebra one-dimensional commutator ideal, three exceptions, is an derivation.

Let $L$ be a finite-dimensional Lie algebra. We say a subalgebra $H$ of $L$ is permutably complemented in $L$ if there is a subalgebra $K$ of $L$ such that $L=H+K$ and $Hcap K=0$. Also, if every subalgebra of $L$ is permutably complemented in $L$, then $L$ is called completely factorisable. In this article, we consider the influence of these concepts on the structure of a Lie algebra, in partic...

We give an explicit description of a set of irreducible representations of a Weyl group which parametrizes the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre concerning the conjugacy class of a power of a unipotent element in a connected reductive group.

In this paper we present interpretations of Lommel polynomials and their derivatives. A combinatorial interpretation uses matchings in graphs. This gives an interpretation for the derivatives as well. Then Lommel polynomials are considered from the point of view of operator calculus. A step-3 nilpotent Lie algebra and finite-difference operators arise in the analysis.

Each matrix A in GLn(Z) naturally defines an automorphism f of the free r-step nilpotent Lie algebra fn,r. We study the relationship between the matrix A and the eigenvalues and rational invariant subspaces for f. We give applications to the study of Anosov automorphisms.

Let G be a simply connected connected real nilpotent Lie group with Lie algebra g, H a connected closed subgroup of G with Lie algebra h and β ∈ h∗ satisfying β([h, h]) = {0}. Let χβ be the unitary character of H with differential 2 √ −1πβ at the origin. Let τ ≡ IndHχβ be the unitary representation of G induced from the character χβ of H. We consider the algebra D(G,H, β) of differential operat...

Let N be a non-commutative, simply connected, connected, two-step nilpotent Lie group with Lie algebra n such that n = a⊕ b⊕ z, [a, b] ⊆ z, the algebras a, b, z are abelian, a = R-span {X1, X2, · · · , Xd} , and b = R-span {Y1, Y2, · · · , Yd} . Also, we assume that det [[Xi, Yj ]]1≤i,j≤d is a non-vanishing homogeneous polynomial in the unknowns Z1, · · · , Zn−2d where {Z1, · · · , Zn−2d} is a ...