It is shown how the de-Sitter Relativistic behaviour of the hyperbolic trajectory of Pioneer, due to the expansion of the Universe (non-vanishing cosmological constant), is the underlying physical reason for the observed anomalous acceleration of the Pioneer spacecraft of the order of c/RH ∼ 8.74 × 10−10 m/s2, where c is the speed of light and RH is the present Hubble scale. We display the expl...

In this paper we are interested in the order structure induced by the relations ’before’ and ’meets’ of Allen’s interval algebra. We provide an abstract definition of this kind of order structure called an interval order. We prove that every interval order is isomorphic to the corresponding order on a set of finite intervals over a linear order without endpoints. As a consequence of this charac...

Let G be the planar Galilean conformal algebra and G˜ its universal central extension. Then (resp. G˜) admits a triangular decomposition: G=G+?G0?G? G˜=G˜+?G˜0?G˜?). In this paper, we study generic Whittaker G-modules G˜-modules) of type ?, where ?:G+?G˜+?C is Lie homomorphism. We classify isomorphism classes modules. Moreover, show that module ? simple if only nonsingular. For nonsingular case...

Abstract Let K be a number field, let A finite-dimensional -algebra, $\operatorname {\mathrm {J}}(A)$ denote the Jacobson radical of and $\Lambda $ an $\mathcal {O}_{K}$ -order in . Suppose that each simple component semisimple -algebra $A/{\operatorname {J}}(A)}$ is isomorphic to matrix ring over field. Under this hypothesis on , we give algorithm that, given two -lattices X Y determines wheth...

In this paper, a semigroup algebra consisting of polynomial expressions with coefficients in field F and exponents an additive submonoid M Q≥0 is called Puiseux denoted by F[M]. Here we study the atomic structure algebras. To begin with, answer isomorphism problem for class algebras, that is, show if two algebras F[M1] F[M2] are isomorphic, then monoids M1 M2 must be isomorphic. Then construct ...

We determine the periodic cyclic homology of the Iwahori-Hecke algebras Hq, for q ∈ C∗ not a “proper root of unity.” (In this paper, by a proper root of unity we shall mean a root of unity other than 1.) Our method is based on a general result on periodic cyclic homology, which states that a “weakly spectrum preserving” morphism of finite type algebras induces an isomorphism in periodic cyclic ...

This paper is a part of the series [KL]; however, it can be read independently of the first two parts. In [D3], Drinfeld proved the existence of an equivalence between a tensor category of representations of a quantum group over C[[ ro]] and a tensor category of representations of an undeformed enveloping algebra over C[[ro]] , in which the associativity constraints are given by the Knizhnik-Za...

In this paper we look at the K-theory of a specific C*-algebra closely related to the irrational rotation algebra. Also it is shown that any automorphism of a C*-algebra A induces group automorphisms of K_{1}(A) amd K_{0}(A) in an obvious way. An interesting problem for any C*-algebra A is to find out whether, given an automorphism of K_{0}(A) and an automorphism of K_{1}(A), we can lift them t...

To any finite group G SL2ðCÞ and each element t in the center of the group algebra of G, we associate a category, CohðP G;t ;PÞ: It is defined as a suitable quotient of the category of graded modules over (a graded version of) the deformed preprojective algebra introduced by Crawley-Boevey and Holland. The category CohðP G;t ;PÞ should be thought of as the category of coherent sheaves on a ‘non...

We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine) Hecke-Clifford algebras of Olshanski and Jones-Nazarov. Relation between the spin (affine) Hecke algebra and a nonstandard presentation of the usual (affine) Hecke alge...