Tensor products of nonassociative cyclic algebras

We study the tensor product of an associative and a nonassociative cyclic algebra. The condition for the tensor product to be a division algebra equals the classical one for the tensor product of two associative cyclic algebras by Albert or Jacobson, if the base field contains a suitable root of unity. Stronger conditions are obtained in special cases. Applications to space–time block coding are discussed

Albert algebras over curves of genus zero and one

Albert algebras and other Jordan algebras are constructed over curves of genus zero and one, using a generalization of the Tits process and the first Tits construction due to Achhammer.Comment: 37 page

Experimental Design for Variable Selection in data bases

This paper analyses the influence of 13 stylized facts of the German economy on the West German business cycles from 1955 to 1994. The method used in this investigation is Statistical Experimental Design with orthogonal factors. We are looking for all existing Plackett-Burman designs realizable by coded observations of these data. The plans are then analysed by regression with forward selection and various classification methods to extract the relevant variables for separating upswing and downswing of the cycles. The results are compared with already existing studies on this topic. --

Absolutely convex modules and Saks spaces

AbstractAbsolutely or totally convex modules are a canonical generalization of absolutely or countably absolutely convex sets in linear spaces. There are canonical connections between the category of absolutely convex modules and the category of Saks spaces, each of which is given by a pair of adjoint functors. Corresponding results hold for totally convex modules

D-optimal plans in observational studies

This paper investigates the use of Design of Experiments in observational studies in order to select informative observations and features for classification. D-optimal plans are searched for in existing data and based on these plans the variables most relevant for classification are determined. The adapted models are then compared with respect to their predictive accuracy on an independent test sample. Eight different data sets are investigated by this method. --D-optimality,Genetic Algorithm,Prototypes,Feature Selection

A generalisation of Amitsur's A-polynomials

summary:We find examples of polynomials $f\in D[t;\sigma ,\delta ]$ whose eigenring $\mathcal {E}(f)$ is a central simple algebra over the field $F = C \cap \mathrm {Fix}(\sigma ) \cap \mathrm {Const}(\delta )$

Norm Principles for Forms of Higher Degree Permitting Composition

Let F be a field of characteristic 0 or greater than d. Scharlau’s norm principle holds for finite field extensions K over F, for certain forms φ of degree d over F which permit composition

Diagonal Forms of Higher Degree Over Function Fields of p-adic Curves

We investigate diagonal forms of degree d over the function field F of a smooth projective p-adic curve: if a form is isotropic over the completion of F with respect to each discrete valuation of F , then it is isotropic over certain fields F_U , F_P and F_p. These fields appear naturally when applying the methodology of patching; F is the inverse limit of the finite inverse system of fields {F_U , F_P , F_p}. Our observations complement some known bounds on the higher u-invariant of diagonal forms of degree d. We only consider diagonal forms of degree d over fields of characteristic not dividing d!

Nonassociative differential extensions of characteristic p

Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a finite-dimensional central division algebra over F and give a criterium for these algebras to be division. As special cases, we obtain classical results for associative algebras by Amitsur and Jacobson. We construct families of nonassociative division algebras which can be viewed as generalizations of associative cyclic extensions of a purely inseparable field extension of exponent one or a central division algebra. Division algebras which are nonassociative cyclic extensions of a purely inseparable field extension of exponent one are particularly easy to obtain

The automorphisms of Petit's algebras

Let σ be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t; σ]=fK[t; σ] obtained when the twisted polynomialf 2 K[t; σ] is invariant, and were first defined by Petit. We compute all their automorphisms if V commutes with all automorphisms in AutF (K) and n < m-1. In thecase where K=F is a finite Galois field extension, we obtain more detailed information on the structure of the automorphism groups of these nonassociative unital algebras over F. We also briefly investigate when two such algebras are isomorphic