Isomorphism of Commutative Group Algebras of Finite Abelian Groups

Let a commutative ring R be a direct product of indecomposable rings with identity and let G be a finite abelian p-group. In the present paper we give a complete system of invariants of the group algebra RG of G over R when p is an invertible element in R. These investigations extend some classical results of Berman (1953 and 1958), Sehgal (1970) and Karpilovsky (1984) as well as a result of Mollov (1986).

Sylow P-Subgroups of Abelian Group Rings

2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.

Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves

2000 Mathematics Subject Classification: Primary 34C07, secondary 34C08.

Complex Hyperbolic Surfaces of Abelian Type

2000 Mathematics Subject Classification: 11G15, 11G18, 14H52, 14J25, 32L07.

Multipliers on Spaces of Functions on a Locally Compact Abelian Group with Values in a Hilbert Space

2000 Mathematics Subject Classification: Primary 43A22, 43A25.

The simultaneous extraction of multiple social categories from unfamiliar faces

The research was supported by an award from the Experimental Psychology Society's Small Grant scheme.

The simultaneous extraction of multiple social categories from unfamiliar faces

The research was supported by an award from the Experimental Psychology Society's Small Grant scheme.

Non-Verbal Categories. Analysis of an Galician Oral Narrative

Based on the concept of the triple basic structure of human communication by Poyatos (1994a, 1994b) and on the analytical and theoretical implications that derive from this, the present paper conceives the human communication as an indivisible whole in which verbal communication can not be separated from body behavior. This paper analyzes nonverbal categories used in oral communication. The corpus consists of an oral narration in Galician from which we highlighted certain kinemes (minimum units of body movement with meaning) by using the model proposed by Bouvet (2001), in order to explain the non-verbal categories with examples taken from said recordings.

Splitting monoidal stable model categories

If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S,S]C. An idempotent e of this ring will split the homotopy category: [X,Y]C≅e[X,Y]C⊕(1−e)[X,Y]C. We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to LeSC×L(1−e)SC and [X,Y]LeSC≅e[X,Y]C. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is.

A monoidal algebraic model for rational SO(2)-spectra

The category of rational SO(2)--equivariant spectra admits an algebraic model. That is, there is an abelian category A(SO(2)) whose derived category is equivalent to the homotopy category of rational$SO(2)--equivariant spectra. An important question is: does this algebraic model capture the smash product of spectra? The category A(SO(2)) is known as Greenlees' standard model, it is an abelian category that has no projective objects and is constructed from modules over a non--Noetherian ring. As a consequence, the standard techniques for constructing a monoidal model structure cannot be applied. In this paper a monoidal model structure on A(SO(2)) is constructed and the derived tensor product on the homotopy category is shown to be compatible with the smash product of spectra. The method used is related to techniques developed by the author in earlier joint work with Roitzheim. That work constructed a monoidal model structure on Franke's exotic model for the K_(p)--local stable homotopy category. A monoidal Quillen equivalence to a simpler monoidal model category that has explicit generating sets is also given. Having monoidal model structures on the two categories removes a serious obstruction to constructing a series of monoidal Quillen equivalences between the algebraic model and rational SO(2)--equivariant spectra.

Rational O(2)–Equivariant Spectra

The category of rational O(2)-equivariant cohomology theories has an algebraic model A(O(2)), as established by work of Greenlees. That is, there is an equivalence of categories between the homotopy category of rational O(2)-equivariant spectra and the derived category of the abelian model DA(O(2)). In this paper we lift this equivalence of homotopy categories to the level of Quillen equivalences of model categories. This Quillen equivalence is also compatible with the Adams short exact sequence of the algebraic model.

Categories, Allegories, and Circuit Design

Languages based upon binary relations offer an appealing setting for constructing programs from specifications. For example, working with relations rather than functions allows specifications to be more abstract (for example, many programs have a natural specification using the converse operator on relations), and affords a natural treatment of non-determinism in specifications. In this paper we present a novel pictorial interpretation of relational terms as simple pictures of circuits, and a soundness/completeness result that allows relational equations to be proved by pictorial reasoning.