Related papers: Real operator algebras and real positive maps
The problem of equivalency for linear differential operators of the first order is discussed.
This survey provides an elementary introduction to operads and to their applications in homotopical algebra. The aim is to explain how the notion of an operad was prompted by the necessity to have an algebraic object which encodes higher…
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
We present recent progress in theory of local conformal nets which is an operator algebraic approach to study chiral conformal field theory. We emphasize representation theoretic aspects and relations to theory of vertex operator algebras…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
We investigate a general structure theory for a vertex operator algebra. We discuss the center and blocks, the Jacobson radical and solvable radical and local vertex operator algebras. The main consequence of our structure theory is that if…
In Quantum Mechanics operators must be hermitian and, in a direct product space, symmetric. These properties are saved by Lie algebra operators but not by those of quantum algebras. A possible correspondence between observables and quantum…
A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lueders - von Neumann quantum…
The goal of this paper is to present an algebraic approach to the basic results of the theory of linear recurrence relations. This approach is based on the ideas from the theory of representations of one endomorphisms (a special case of…
The purpose of this paper is to continue the study of chief factors of a Lie algebra and to prove a further strengthening of the Jordan-H\"older Theorem for chief series.
We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
Real linear operators emerge in a range of mathematical physics applications. In this paper spectral questions of compact real linear operators are addressed. A Lomonosov-type invariant subspace theorem for antilinear compact operators is…
In this paper we study some properties of the field of rational pseudo-differential operators on a field and some other related rings. As an application we reconstruct the Kac co-cycle on the Lie algebra of differential operators on a…
In this paper we consider a one quartic operator on the $\mathbb{R}^2$ with positive coefficients. Positive fixed points for a quartic operator, were investigated. Theorems on number of positive fixed points of the quartic operator, are…
Let X a proper smooth curve over the field of complex numbers. Localization of the Heisenberg algebra gives the algebra of global sections of the ring of differential operators on the Jacobian J of X. It seems natural to ask for same kind…
In a recent paper we showed that a subspace of a real JBW*-triple is an M-summand if and only if it is a weak*-closed triple ideal. As a consequence, M-ideals of real JB*-triples, including real C*-algebras, real JB*-algebras and real TROs,…
In this paper we present the principal construction of the vertex operator representation for toroidal Lie algebras.
We formalize the quantum arithmetic, i.e. a relationship between number theory and operator algebras. Namely, it is proved that rational projective varieties are dual to the $C^*$-algebras with real multiplication. Our construction fits all…
For ring of differential operators on smooth affine algebraic variety over perfect field of prime characteristic a set of algebra generators and a set of defining relations are found explicitly.