Algebras determined by their supports

In this paper, we introduce and study a class of algebras which we call ada algebras. An artin algebra is ada if every indecomposable projective and every indecomposable injective module lies in the union of the left and the right parts of the module category. We describe the Auslander–Reiten components of an ada algebra which is not quasi-tilted, showing in particular that its representation theory is entirely contained in that of its left and right supports, which are both tilted algebras. Also, we prove that an ada algebra over an algebraically closed field is simply connected if and only if its first Hochschild cohomology group vanishes.     

Modular Group Algebras with Almost Maximal Lie Nilpotency Indices

Let be a field of positive characteristic and the group algebra of a group . It is known that, if is Lie nilpotent, then its upper (and lower) Lie nilpotency index is at most , where is the order of the commutator subgroup. The authors previously determined those groups for which this index is maximal and here they determine the groups for which it is `almost maximal', that is, it takes the next highest possible value, namely .Presented by V. Dl a b.Dedicated to Professor Vjacheslav Rudko on his 65th birthday.The research was supported by OTKA No. T 037202, No. T 038059 and Italian National Research Project “Group Theory and Application.”     

Weyl formula for multi-quasi-elliptic operators. of Schrödinger type

In this work we consider a general class of Schr?dinger type operators, associated with multi-quasi-elliptic symbols. We give a precise estimate of the remainder of the so-called Weyl asymptotic formula for the eigenvalues of these operators. In order to reach our aim, we use the Weyl–H?rmander calculus, with locally temperate metrics and weights, and interpolation techniques. Received: February 14, 2000; in final form: October 29, 2000?Published online: July 13, 2001     

On Taylor series and Kapteyn series of the first and second type

We study the relation between the coefficients of Taylor series and Kapteyn series representing the same function. We compute explicit formulas for expressing one in terms of the other and give examples to illustrate our method.     

Instabilities of micellar systems under homogeneous and non-homogeneous flow conditions

The rheological behavior of a cetylpyridinium chloride 100 mmol l^–1/sodium salicylate 60 mmol l^–1 aqueous solution was studied in this work under homogeneous (cone and plate) and non-homogeneous flow conditions (vane-bob and capillary rheometers), respectively. Instabilities consistent with non-monotonic flow curves were observed in all cases and the solution exhibited similar behavior under the different flow conditions. Hysteresis and the sigmoidal flow curve suggested as characteristic of systems that show constitutive instabilities were observed when running cycles of increasing and decreasing stress or shear rate, respectively. This information, together with a detailed determination of steady states at shear stresses close to the onset of the instabilities, allowed one to show unequivocally that "top and bottom jumping" are the mechanisms to trigger the instabilities in this micellar system. It is shown in addition that there is not a true plateau region in between the "top and bottom jumping". Finally, the flow behavior beyond the upturn seemed to be unstable and was found accompanied by an apparent violation of the no-slip boundary condition.     

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Dfⁿ(f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d2 and critical point c of order ℓ>1. As an application we prove that f exhibits exponential decay of geometry if and only if ℓ2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet–Eckmann condition.     

On a conjecture of Whittaker concerning uniformization of hyperelliptic curves

This article concerns an old conjecture due to E. T. Whittaker, aiming to describe the group uniformizing an arbitrary hyperelliptic Riemann surface as an index two subgroup of the monodromy group of an explicit second order linear differential equation with singularities at the values .

Whittaker and collaborators in the thirties, and R. Rankin some twenty years later, were able to prove the conjecture for several families of hyperelliptic surfaces, characterized by the fact that they admit a large group of symmetries. However, general results of the analytic theory of moduli of Riemann surfaces, developed later, imply that Whittaker's conjecture cannot be true in its full generality.

Recently, numerical computations have shown that Whittaker's prediction is incorrect for random surfaces, and in fact it has been conjectured that it only holds for the known cases of surfaces with a large group of automorphisms.

The main goal of this paper is to prove that having many automorphisms is not a necessary condition for a surface to satisfy Whittaker's conjecture.

     

Group Rings Whose Symmetric Units Generate an n-Engel Group

Let F be an infinite field of characteristic different from 2 and G a torsion group. Write 𝒰⁺(FG) for the set of units in the group ring FG that are symmetric with respect to the classical involution induced from the map g ? g ^?1, for all g ∈ G. We classify the groups such that ?𝒰⁺(FG)? is n-Engel.