相关论文: Term Algebras, Canonical Representations and Diffe…

For any finite dimensional basic associative algebra, we study the presentation spaces and their relation with the representation spaces. We prove two propositions about a general presentation, one on its subrepresentations and the other on…

Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…

In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…

We develop the representation theory of a finite semigroup over an arbitrary commutative semiring with unit, in particular classifying the irreducible and minimal representations. The results for an arbitrary semiring are as good as the…

For some research questions that involve Spin(p, q) representation theory, using symbolic algebra based techniques might be an attractive option for simplifying and manipulating expressions. Yet, for some such problems, especially as they…

Simplification of expressions in computer algebra systems often involves a step known as "canonicalisation", which reduces equivalent expressions to the same form. However, such forms may not be natural from the perspective of a…

A diverse collection of fusion categories may be realized by the representation theory of quantum groups. There is substantial literature where one will find detailed constructions of quantum groups, and proofs of the…

This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial…

Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They…

Diagrammatic, analogical or iconic representations are often contrasted with linguistic or logical representations, in which the shape of the symbols is arbitrary. The aim of this paper is to make a case for the usefulness of diagrams in…

These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…

The present work attempts both a review of previous methods for transferring digital and symbolic computations in an analog or optical substrate and also to offer certain alternatives not yet fully explored. The essential difference from…

In this paper, we review the theory of time space-harmonic polynomials developed by using a symbolic device known in the literature as the classical umbral calculus. The advantage of this symbolic tool is twofold. First a moment…

The representation ring of an affine algebraic group scheme can be endowed with the structure of a (special) $\lambda$-ring. We show that the same is true for the ring of symmetric representations, i.e. for the Grothendieck-Witt ring of the…

We present a general framework in the setting of difference ring extensions that enables one to find improved representations of indefinite nested sums such that the arising denominators within the summands have reduced degrees. The…

An algebraic framework in which to study infinite sums is proposed, complementing and augmenting the usual topological tools. The framework subsumes numerous examples in the literature. It is developed using many varied examples, with a…

The classical number system encodes magnitude using a single scalar value whose sign positive or negative has remained conceptually unchanged for centuries. This work introduces Multisign Algebra, a mathematical generalization of the sign…

In this paper, extending our earlier program, we derive maximal canonical extensions for multiplicative summations into algebraically closed fields. We show that there is a well-defined analogue to minimal polynomials for a series algebraic…

The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…