The theory of equitable partitions of graphs has a number of significant applications. We develop an extension of this theory to matrix algebras acting on the space of functions on a finite set. Our main application of this is to establish a quotient theorem which has, as special cases, the s tandard results on quotients in association schemes and distance regular graphs. © 1995 Academic Press,...

A magnetic monopole is placed at the centre of a ball whose surface S 2 is tiled by the symmetry group, Γ, of a regular solid. The quantum mechanics on the two-dimensional quotient S 2 /Γ is developed and the monopole charge is found to be quantised in an expected manner. The heat-kernel and ζ–functions are evaluated and the Casimir energy is computed. Numerical approaches to the calculation of...

Let C be a complex affine reduced curve, and denote by H1(C) its first truncated cohomology group, i.e. the quotient of all regular differential 1-forms by exact 1-forms. First we introduce a nonnegative invariant μ(C, x) that measures the complexity of the singularity of C at the point x, and we establish the following formula: dim H(C) = dim H1(C) + ∑

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...

The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is us...

Let R be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented R-modules that are closed under extensions. We also classify abelian subcategories of arbitrary R-modules that are closed under extensions and coproducts, when R is commutative and Noetherian. The method relies on comparison with ...

In this paper, we introduce a new homological invariant called quasi-projective dimension, which is generalization of projective dimension. We discuss various properties Among other things, prove the following. (1) Over quotient regular local ring by sequence, every finitely generated module has finite (2) The Auslander--Buchsbaum formula and depth for modules dimension remain valid (3) Several...

In this note we first show that for a right (resp. left) Ore ring R and an automorphism σ of R, if R is σ-skew McCoy then the classical right (resp. left) quotient ring Q(R) of R is σ̄-skew McCoy. This gives a positive answer to the question posed in Başer et al. [1]. We also characterize semiprime right Goldie (von Neumann regular) McCoy (σ-skew McCoy) rings.

We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor HomC(T, −), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left and right fractions. It follows that the Gabriel-Zisman localisation of the quotient at the class of regular morphisms is abelian. We show that it is equiv...