Related papers: Coding theory applied to KU-algebras
We define E-theory for separable C*-algebras over second countable topological spaces and establish its basic properties. This includes an approximation theorem that relates the E-theory over a general space to the E-theories over finite…
We develop integration theory for integrating functions taking values into a Dedekind complete unital $f$-algebra $\mathbb{L}$ with respect to $\mathbb{L}$-valued measures. We then discuss and prove completeness results of…
We develop a new general framework for algebras and clones, called Universal Clone Algebra. Algebras and clones of finitary operations are to Universal Algebra what t-algebras and clone algebras are to Universal Clone Algebra. Clone…
We propose a type-theoretic framework for describing and proving properties of quantum computations, in particular those presented as quantum circuits. Our proposal is based on an observation that, in the polymorphic type system of Coq,…
Boolean calculus has been studied extensively in the past in the context of switching circuits, error-correcting codes etc. This work generalizes several approaches to defining a differential calculus for Boolean functions. A unified theory…
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
The quantum integrable systems associated with the quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{\, l + 1}))$ are considered. The factorized form of the transfer operators related to the infinite dimensional evaluation…
We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.
Some introductory concepts and basic definitions of the Lie superalgebras and their quantum deformations are exposed. Especially the induced representation methods in both cases are described. Based on the Kac representation theory we have…
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov…
Through the subsequent discussion we consider a certain particular sort of (topological) algebras, which may substitute the `` structure sheaf algebras'' in many--in point of fact, in all--the situations of a geometrical character that…
Let D be a domain with quotient field K and A a D-algebra. We call a polynomial with coefficients in K that maps every element of A to an element of A "integer-valued on A". For commutative A we also consider integer-valued polynomials in…
In this paper, a new invariant was built towards the classification of separable C*-algebras of real rank zero, which we call latticed total K-theory. A classification theorem is given in terms of such an invariant for a large class of…
A theory of canonical basis for a two-parameter quantum algebra is developed in parallel with the one in one-parameter case. A geometric construction of the negative part of a two-parameter quantum algebra is given by using mixed perverse…
We introduce a notion of Krein C*-module over a C*-algebra and more generally over a Krein C*-algebra. Some properties of Krein C*-modules and their categories are investigated.
We continue the study of the effective content of $K$-theory for C*-algebras, with a focus on AF algebras. We show that from a c.e. presentation of an AF algebra it is possible to compute a representation of the algebra as an inductive…
We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the…
Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions,…
The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…