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We introduce a systematic approach for the resummation of perturbative series which involve large logarithms not only due to large invariant mass ratios but large rapidities as well. Series of this form can appear in a variety of gauge…
It is widely understood that the quotient space of a topological group action can have a complicated combinatorial structure, indexed somehow by the sotropy groups of the action, but how best to record this structure seems unclear. This…
We reformulate the statement of the Feit-Thompson theorem in terms of diagrams in the category of finite groups, namely iterations of the Quillen lifting property with respect to particular morphisms.
This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…
Functor morphing provides a method to translate complex representations of automorphism groups of finite modules over finite rings to representations of automorphism groups of functors in some abelian category. In this paper we give an…
Given a finitely-generated group G, and a finite group \Gamma, Philip Hall defined \delta_\Gamma to be the number of factor groups of G that are isomorphic to \Gamma. We show how to compute the Hall invariants by cohomological and…
We study affine Grassmannians for ramified triality groups. These groups are of type ${}^3D_4$, so they are forms of the orthogonal or the spin groups in 8 variables. They can be given as automorphisms of certain twisted composition…
For a manifold M we define a structure on the group action of Diff(M) on the smooth functions on M which reduces to the usual differential geometry upon differentiation at zero along the one-parameter groups of Diff(M). This ``integrated…
A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…
A notion of degeneration of elements in groups is introduced. It is used to parametrize the orbits in a finite abelian group under its full automorphism group by a finite distributive lattice. A pictorial description of this lattice leads…
The attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
We investigate the theory of affine group schemes over a symmetric tensor category, with particular attention to the tangent space at the identity. We show that this carries the structure of a restricted Lie algebra, and can be viewed as…
In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be…
This paper introduces a description of Endomorphisms of the translation group in an affine plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and…
We give an algorithm which computes a presentation for a subgroup, denoted $\AM_{g,1,p}$, of the automorphism group of a free group. It is known that $\AM_{g,1,p}$ is isomorphic to the mapping-class group of an orientable genus-$g$ surface…
The regular objects in various categories, such as maps, hypermaps or covering spaces, can be identified with the normal subgroups N of a given group \Gamma, with quotient group isomorphic to \Gamma/N. It is shown how to enumerate such…
Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…
A definition is offered of the factorial characters of the general linear group, the symplectic group and the orthogonal group in an odd dimensional space. It is shown that these characters satisfy certain flagged Jacobi-Trudi identities.…
In this paper, for given an algebraic theory $T$ whose category $C$ of models is semi-abelian, we consider the topological models of $T$ called topological $T$-algebras and obtain some results related to the fundamental groups of…
In this paper we develop the theory of topological categories over a base category, that is, a theory of topological functors. Our notion of topological functor is similar to (but not the same) the existing notions in the literature (see…