Involutive distributions of evolutionary vector fields that belong to images of matrix operators in total derivatives are considered and some classifications of the operators are obtained. The weak compatibility of these operators is an analog of the Poisson pencils for the Hamiltonian structures, while the commutation closure of sums of the images for N -tuples of the operators, which is the s...

We investigate the possibility of giving a computational interpretation of an involutive negation in classical natural deduction. We first show why this cannot be simply achieved by adding ¬¬A = A to typed λ-calculus: the main obstacle is that an involutive negation cannot be a particular case of implication at the computational level. It means that one has to go out typed λ-calculus in order t...

The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2-category theory, such as versions of algebra, limit, colimit, and adjunction, are necessary for this definition. The structure present on the class C of rigged surfaces...

Recently, Jensen [3], Lazar [4] and Rothwell [6] have investigated in detail the structure of scattered C*-algebras which can be regarded as the most elementary generalization of the finite dimensional involutive algebras. A C*-algebra si is called scattered if every positive functional of si is the sum of a sequence of pure functionals. The object of this note is to give a short proof of a nat...

Let g be a complex, semisimple Lie algebra, with an involutive automorphism θ and set k = Ker(θ − I), p = Ker(θ + I). We consider the differential operators, D(p) , on p that are invariant under the action of the adjoint group K of k. Write τ : k → Der(p) for the differential of this action. Then we prove, for the class of symmetric pairs (g, k) considered by Sekiguchi [32], that ̆ d ∈ D(p) : d ...

Buchberger’s algorithm for computing a Gröbner basis solves the ideal membership problem over commutative polynomial rings. In the early 1990’s, an alternative to this algorithm was found, namely the involutive basis algorithm, which provides a Gröbner basis with extra combinatorial properties. Buchberger’s work was generalised to noncommutative polynomial rings by Bergman and Mora during the 1...