ALGEBRAIC ASPECTS OF SPECTRAL THEORY

Algebraic Aspects of Spectral Theory

We describe some aspects of spectral theory that involve algebraic considerations but need no analysis. Some of the important applications of the results are to the algebra of n× n matrices with entries that are polynomials or more general analytic functions. Short title: Algebraic Spectral Theory MSC subject classification: 47A56, 47C05, 15A22, 16Sxx, 16Bxx

Constructive aspects of algebraic euclidean field theory

This paper is concerned with constructive and structural aspects of euclidean field theory. We present a C*-algebraic approach to lattice field theory. Concepts like block spin transformations, action, effective action, and continuum limits are generalized and reformulated within the C*-algebraic setup. Our approach allows to relate to each family of lattice models a set of continuum limits whi...

Algebraic aspects of higher nonabelian Hodge theory

Algebraic and topological aspects of quasi-prime ideals

In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...

Some aspects of the algebraic theory of quadratic forms

There are many good references for this material including [EKM], [L], [Pf] and [S]. 1 Quadratic forms Let k be a field with char k = 2. Definition 1.1. A quadratic form q : V → k on a finite-dimensional vector space V over k is a map satisfying: 1. q(λv) = λ 2 q(v) for v ∈ V , λ ∈ k. 2. The map b q : V × V → k, defined by b q (v, w) = 1 2 [q(v + w) − q(v) − q(w)] is bilinear. We denote a quadr...