相关论文: Algebra generators and information theory

In this short note, we mimic the proof of the simplicity of the theory ACFA of generic difference fields in order to provide a criterion, valid for certain theories of pure fields and fields equipped with operators, which shows that a…

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…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…

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…

According to the basic idea of category theory, any Einstein algebra, essentially an algebraic formulation of general relativity, can be considered from the point of view of any object of the category of smooth algebras; such an object is…

We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result for simplicial algebras over these theories, showing…

We give an accessible introduction into the theory of lower central series of associative algebras, exhibiting the interplay between algebra, geometry and representation theory that is characteristic for this subject, and to discuss some…

The representation theory for categorical groups is constructed. Each categorical group determines a monoidal bicategory of representations. Typically, these categories contain representations which are indecomposable but not irreducible. A…

Let V be a finite dimensional complex superspace and G a simple (or a ``close'' to simple) Lie superalgebra of matrix type, i.e., a Lie subsuperalgebra in GL(V). Under the classical invariant theory for G we mean the description of…

In this work we generalize the concept of product by generators to the class of solvable Lie algebras. We analyze the number of invariants by the coadjoint representation by means of Maurer-Cartan equations and give some applications to…

It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…

For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…

We define a certain abstract planar algebra by generators and relations, study various aspects of its structure, and then identify it with Jones' spin planar algebra.

We generalise the notion of separable equivalence, originally presented by Linckelmann (2011), to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we…

This work adapts the equivalent definitions of division algebras over a field into multiple types of division algebras in a monoidal category. Examples and consequences of these definitions are then established in various monoidal settings.

Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…

Using the classification theorem due to Kac we prove that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by one element.

A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This…

In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has…

Algebraic basics on Temperley-Lieb algebras are proved in an elementary and straightforward way with the help of tensor categories behind them.