相关论文: Notes on normed algebras

These are the notes of an informal talk in Bonn describing how to define an analogue of vertex algebras in higher dimensions.

Fixed point subalgebras of finite dimensional factor algebras of algebras of polynomials in n indeterminates over the finite field $\mathbb F_2$ (with respect to all $\mathbb F_2$-algebra automorphisms) are fully described.

In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.

There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…

We show how the matrix algebra notions of determinant, spectrum, and Hermitian conjugation transfer to the Clifford algebra and to differential forms on parallelisable manifolds.

These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…

This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…

We survey the development and status quo of a subject best described as "generic representation theory of finite dimensional algebras", which started taking shape in the early 1980s. Let $\Lambda$ be a finite dimensional algebra over an…

There is a connection between *-representations of algebras associated with graphs and the problem about the spectrum of a sum of Hermitian operators (spectral problem). For algebras associated with extended Dynkin graphs we give an…

This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…

We give an interpretation of J-spaces in terms of symmetric spectra in symmetric sequences. As application we show how one can define graded endomorphism objects in a general situation. As example we discuss the motivic bigraded…

We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.

All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.

The uniform norm on a uniform normed Q-algebra is the only uniform Q-algebra norm on it. The uniform norm on a regular uniform normed Q-algebra with unit is the only uniform norm on it. Let A be a uniform topological algebra whose spectrum…

Using the algebraic classification of all $2$-dimensional algebras, we give the algebraic classification of all $2$-dimensional rigid, conservative and terminal algebras over an algebraically closed field of characteristic 0. We have the…

This paper continues the work which attempts to understand the general properties of the graded algebras associated with Hecke symmetries without a restriction on the parameter q of the Hecke relation imposed in earlier results.

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…

A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…

For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.