6,718 research outputs found

### Derivations of the Lie Algebras of Differential Operators

This paper encloses a complete and explicit description of the derivations of
the Lie algebra D(M) of all linear differential operators of a smooth manifold
M, of its Lie subalgebra D^1(M) of all linear first-order differential
operators of M, and of the Poisson algebra S(M)=Pol(T*M) of all polynomial
functions on T*M, the symbols of the operators in D(M). It turns out that, in
terms of the Chevalley cohomology, H^1(D(M),D(M))=H^1_{DR}(M),
H^1(D^1(M),D^1(M))=H^1_{DR}(M)\oplus\R^2, and
H^1(S(M),S(M))=H^1_{DR}(M)\oplus\R. The problem of distinguishing those
derivations that generate one-parameter groups of automorphisms and describing
these one-parameter groups is also solved.Comment: LaTeX, 15 page

### Lie algebroid structures on a class of affine bundles

We introduce the notion of a Lie algebroid structure on an affine bundle
whose base manifold is fibred over the real numbers. It is argued that this is
the framework which one needs for coming to a time-dependent generalization of
the theory of Lagrangian systems on Lie algebroids. An extensive discussion is
given of a way one can think of forms acting on sections of the affine bundle.
It is further shown that the affine Lie algebroid structure gives rise to a
coboundary operator on such forms. The concept of admissible curves and
dynamical systems whose integral curves are admissible, brings an associated
affine bundle into the picture, on which one can define in a natural way a
prolongation of the original affine Lie algebroid structure.Comment: 28 page

### Contractions: Nijenhuis and Saletan tensors for general algebraic structures

Generalizations in many directions of the contraction procedure for Lie
algebras introduced by E.J.Saletan are proposed. Products of arbitrary nature,
not necessarily Lie brackets, are considered on sections of finite-dimensional
vector bundles. Saletan contractions of such infinite-dimensional algebras are
obtained via a generalization of the Nijenhuis tensor approach. In particular,
this procedure is applied to Lie algebras, Lie algebroids, and Poisson
structures. There are also results on contractions of n-ary products and
coproducts.Comment: 25 pages, LateX, corrected typo

### Theory for Superconducting Properties of the Cuprates: Doping Dependence of the Electronic Excitations and Shadow States

The superconducting phase of the 2D one-band Hubbard model is studied within
the FLEX approximation and by using an Eliashberg theory. We investigate the
doping dependence of $T_c$, of the gap function $\Delta ({\bf k},\omega)$ and
of the effective pairing interaction. Thus we find that $T_c$ becomes maximal
for $13 \; \%$ doping. In {\it overdoped} systems $T_c$ decreases due to the
weakening of the antiferromagnetic correlations, while in the {\it underdoped}
systems due to the decreasing quasi particle lifetimes. Furthermore, we find
{\it shadow states} below $T_c$ which affect the electronic excitation spectrum
and lead to fine structure in photoemission experiments.Comment: 10 pages (REVTeX) with 5 figures (Postscript

### Modular classes of skew algebroid relations

Skew algebroid is a natural generalization of the concept of Lie algebroid.
In this paper, for a skew algebroid E, its modular class mod(E) is defined in
the classical as well as in the supergeometric formulation. It is proved that
there is a homogeneous nowhere-vanishing 1-density on E* which is invariant
with respect to all Hamiltonian vector fields if and only if E is modular, i.e.
mod(E)=0. Further, relative modular class of a subalgebroid is introduced and
studied together with its application to holonomy, as well as modular class of
a skew algebroid relation. These notions provide, in particular, a unified
approach to the concepts of a modular class of a Lie algebroid morphism and
that of a Poisson map.Comment: 20 page

- …