We describe a class of non-central extensions of the diffeomorphism algebra in N -dimensional spacetime, and construct lowest-energy modules thereof, thus generalizing work of Eswara-Rao and Moody. There is one representation for each representation of V ir⋉̃k0 ĝl(N) (an extension of the semi-direct product). Similar modules are constructed for gauge algebras.

We provide the set of left-invariant minimal unit vector fields on the semi-direct product Rn oP R, where P is a nonsingular diagonal matrix and on the 7 classes of 4-dimensional solvable Lie groups of the form R3 oP R which are unimodular and of type (R).

We prove that the Scott module whose vertex is isomorphic to a direct product of generalized quaternion $2$-group and cyclic Brauer indecomposable. This result generalizes similar results which are obtained for abelian, dihedral, quaternion, semidihedral wreathed vertices.

This paper aims at treating a study on Sylow theorem of different algebraic structures as groups, order group, subgroups, along with the associated notions automorphisms group dihedral split extensions groups and vector spaces arises from varying properties real complex numbers. We must have used theorems this work when it's generalized. Here we discuss possible subgroups in types which will gi...

In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zpr ⋊ Zq, for p and q prime. We first present a classification of these groups in five classes. Then, we describe a polynomial-time quantum algorithm solving the HSP over all the groups of one of these classes: the groups of the form Zpr ⋊ Zp, where p is an odd prime. Our algorithm works ev...

Let G1 × G2 be a subgroup of SO3(R) such that the two factors G1 and G2 are non-trivial groups. We show that if G1 × G2 is not abelian, then one factor is the (abelian) group of order 2, and the other factor is nonabelian and contains an element of order 2. There exist finite and infinite such non-abelian subgroups. Let F2 be the free group of rank 2. It is well-known that the group SO3(R) has ...

We present GSMPA, a stochastically timed process algebra that enhances the expressiveness of the stochastically timed process algebra EMPA by allowing arbitrarily distributed durations to be directly modeled through the adoption of the mechanism of action identification as well as the adoption of the preselection policy for alternative actions. GSMPA is introduced together with the definition o...

We show that there exist no proper warped product semi-invariant submanifolds in almost paracontact Riemannian manifolds such that totally geodesic submanifold and totally umbilical submanifold of the warped product are invariant and anti-invariant, respectively. Therefore, we consider warped product semi-invariant submanifolds in the form N N⊥×fNT by reversing two factor manifolds NT and N⊥. W...

We have previously introduced Generalized Semi-Markovian Process Algebra (GSMPA), a process algebra based on ST semantics which is capable of expressing durational actions, where durations are expressed by general probability distributions. In this paper we introduce the calculus of Interactive Generalized Semi-Markov Processes (IGSMP), a variant of GSMPA where synchronizable actions are restri...