Introduction. Let VecR be the Lie algebra of smooth vector fields on R. In this talk we will survey some results concerning the action of VecR on modules of differential operators. To begin with, let σ be the two-sided action of VecR on the associative algebra Diff R of smooth differential operators on R: σ(X)T := X ◦ T − T ◦X. This is a derivation action which preserves the order filtration Di...

We identify an explicit set of complete and independent Wilson loop invariants for 2+1 gravity on a three-manifold M = IR × Σ, with Σ a compact oriented Riemann surface of arbitrary genus g. In the derivation we make use of a global cross section of the PSU(1, 1)principal bundle over Teichmüller space given in terms of Fenchel-Nielsen coordinates. 1 address after Aug 94: Sezione INFN di Firenze...

Abstract: Let X be a Banach space. We define the concept of a bi-parameter semigroup on X and its first and second generators. We also study bi-parameter semigroups on Banach algebras. A relation between uniformly continuous bi-parameter semigroups and σ-derivations is also established. It is proved that if {αt,s}t,s 0 is a uniformly continuous bi-parameter semigroup on a Banach algebra X , who...

Intersection types were originally introduced as idempotent, i.e., modulo the equivalence σ ∧σ = σ . In fact, they have been used essentially for semantic purposes, for building filter models for λ -calculus, where the interpretation of types as properties of terms induces naturally the idempotence property. Recently it has been observed that, when dropping idempotency, intersection types can b...

let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

In this paper, it has been proved that for a Noetherian ring R and an automorphism σ of R, an associated prime ideal of R[x, σ] or R[x, x−1, σ] is the extension of its contraction to R and this contraction is the intersection of the orbit under σ of some associated prime ideal of R. The same statement is true for minimal prime ideals also. It has also been proved that for a Noetherian Q-algebra...

The t-channel contribution to the difference of electromagnetic polarizabilities of the nucleon, (α−β)t, can be quantitatively understood in terms of a σ-meson pole in the complex t-plane of the invariant scattering amplitude A1(s, t) with properties of the σ meson as given by the quark-level Nambu–Jona-Lasinio model (NJL). Equivalently, this quantity may be understood in terms of a cut in the ...

A derivation of the Lax pair for the (1 + 1)-dimensional non-linear σ-model is described. Its main benefit is to have a clearer physical origin and to allow the study of a generalization to higher dimensions. PACS: 11.10.Kk, 11.30.-j , 11.30.Ly