Let Cl(OK [G]) denote the locally free class group, that is the group of stable isomorphism classes of locally free OK [G]-modules, where OK is the ring of algebraic integers in the number field K and G is a finite group. We show how to compute the Swan subgroup, T (OK [G]), of Cl(OK [G]) when K = Q(ζp), ζp a primitive p-th root of unity, G = C2, where p is an odd (rational) prime so that hp = ...

We investigate interconnected aspects of hyperderivatives polynomials over finite fields, q -th powers polynomials, and specializations Vandermonde matrices. construct formulas for Carlitz multiplication coefficients using symmetric we prove identities hyperderivative power sums in terms the inverse matrix. As an application these results give a new proof theorem Thakur on explicit Anderson's s...

Abstract. Let −D < −4 denote a fundamental discriminant which is either odd or divisible by 8, so that the canonical Hecke character of Q( √ −D) exists. Let d be a fundamental discriminant prime to D. Let 2k− 1 be an odd natural integer prime to the class number of Q( √ −D). Let χ be the twist of the (2k − 1)th power of a canonical Hecke character of Q( √ −D) by the Kronecker’s symbol n 7→ ( d ...

The positive-energy unitary irreducible representations of the q-deformed conformal algebra Cq = Uq(su(2, 2)) are obtained by appropriate deformation of the classical ones. When the deformation parameter q is N -th root of unity, all these unitary representations become finitedimensional. For this case we discuss in some detail the massless representations, which are also irreducible representa...

Given an odd prime p we show a way to construct large families of polynomials Pq(x) ∈ Q[x], q ∈ C, where C is a set of primes of the form q ≡ 1 mod p and Pq(x) is the irreducible polynomial of the Gaussian periods of degree p in Q(ζq). Examples of these families when p = 7 are worked in detail. We also show, given an integer n ≥ 2 and a prime q ≡ 1 mod 2n, how to represent by matrices the Gauss...

AIM To evaluate the radiographic technical quality of root fillings and the incidence of iatrogenic errors in treatment provided by undergraduate students. METHODOLOGY Endodontic records and periapical radiographs of 759 root filled teeth were selected following exclusion of 25 (3.3%). A final total of 734 cases were used to assess the technical quality of root fillings in 1109 root canals pe...

We study Markov measures and a p-adic random walk with the use of states on the Cuntz algebras Op. Via the GNS-construction, these come from families of representations of Op. We prove that these representations reflect self-similarity especially well. In this paper we consider a Cuntz-Krieger type algebra where the adjacency matrix depends on a parameter q (q = 1 is the case of Cuntz-Krieger)....

An Uq(sl(n)) invariant transfer matrix with periodic boundary conditions is analysed by means of the algebraic nested Bethe ansatz for the case of q being a root of unity. The transfer matrix corresponds to a 2-dimensional vertex model on a torus with topological interaction w.r.t. the 3-dimensional interior of the torus. By means of finite size analysis we find the central charge of the corres...

We consider integrable vertex models whose Boltzmann weights (Rmatrices) are trigonometric solutions to the graded Yang-Baxter equation. As is well known the latter can be generically constructed from quantum affine superalgebras Uq(ĝ). These algebras do not form a symmetry algebra of the model for generic values of the deformation parameter q when periodic boundary conditions are imposed. If q...