Computation of locally free class groups

We show that the locally free class group of an order in a semisimple algebra over a number field is isomorphic to a certain ray class group. This description is then used to present an algorithm that computes the locally free class group. The algorithm is implemented in MAGMA for the case where the algebra is a group ring over the rational numbers.

Double hegemony?

The paper introduces research on transatlantic relations done by neo-Gramscian authors. This research is distinctive by focusing on class in international relations and by using the concept of hegemony in a relational sense. Hegemony is leadership through the active consent of other classes and groups. A central question of this neo-Gramscian research is whether an international class of capitalists has emerged. Some authors have answered in the positive. This paper, however, maintains that hegemony in the international realm is still exercised by the American state, though its foreign economic policies have been greatly influenced by internationally-oriented corporations and that these actors have increasingly found allies among economic elites in other countries. The paper explores the relationship between hegemony by the American state and by internationally-oriented capital groups against the backdrop of transatlantic relations in the post-war period and the currrent debate on labor rights in international trade agreements.

Church-Rosser groups and growing context-sensitive groups

A finitely generated group is called a Church-Rosser group (growing context-sensitive group) if it admits a finitely generated presentation for which the word problem is a Church-Rosser (growing context-sensitive) language. Although the Church-Rosser languages are incomparable to the context-free languages under set inclusion, they strictly contain the class of deterministic context-free languages. As each context-free group language is actually deterministic context-free, it follows that all context-free groups are Church-Rosser groups. As the free abelian group of rank 2 is a non-context-free Church-Rosser group, this inclusion is proper. On the other hand, we show that there are co-context-free groups that are not growing context-sensitive. Also some closure and non-closure properties are established for the classes of Church-Rosser and growing context-sensitive groups. More generally, we also establish some new characterizations and closure properties for the classes of Church-Rosser and growing context-sensitive languages.

Computations in Relative Algebraic K-Groups

Let G be finite group and K a number field or a p-adic field with ring of integers O_K. In the first part of the manuscript we present an algorithm that computes the relative algebraic K-group K_0(O_K[G],K) as an abstract abelian group. We solve the discrete logarithm problem, both in K_0(O_K[G],K) and the locally free class group cl(O_K[G]). All algorithms have been implemented in MAGMA for the case K = \IQ. In the second part of the manuscript we prove formulae for the torsion subgroup of K_0(\IZ[G],\IQ) for large classes of dihedral and quaternion groups.

Computation of relativistic symmetry orbitals for finite double point groups

A program is presented for the construction of relativistic symmetry-adapted molecular basis functions. It is applicable to 36 finite double point groups. The algorithm, based on the projection operator method, automatically generates linearly independent basis sets. Time reversal invariance is included in the program, leading to additional selection rules in the non-relativistic limit.

Pursuing a Developmental State Trade Agenda in a Neo-Liberal Context

This book explains why it was possible for the Worker’s Party (PT) in Brazil and the African National Congress (ANC) in South Africa to pursue a developmental state trade policy, in spite of neoliberal constraints. The major theoretical lenses are three-fold. It applies state theory (macrolevel), policy network analysis (meso-level) and theories on political parties with emphasis on factional politics (micro-level). This book highlights the socio-political relevance of comparatively progressive policy frameworks and expands the debate on how to re-gain national policy space for progressive reform policies even under neoliberal constraints.