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The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…
Let A be a C*-algebra and A** its enveloping von Neumann algebra. C. Akemann suggested a kind of non-commutative topology in which certain projections in A** play the role of open sets. The adjectives "open", "closed", "compact", and…
This paper establishes an equivalence between the halting problem in computability theory and the convergence of power series in mathematical analysis.
In this article, we completely determine the isomorphism classes of lattice vertex operator algebras and the vertex operator subalgebras fixed by a lift of the -1-isometry of the lattice. We also provide similar results for certain even…
In this article, we introduce the Lipschitz bounded approximation property for operator ideals. With this notion, we extend the original work done by Godefroy and Kalton and give some partial answers on the equivalence between the bounded…
We discuss some different results on Sidon-type inequalities and on the space of quasi-continuous functions.
Consider an infinite-dimensional linear space equipped with a Gaussian measure and the group $GL(\infty)$ of linear transformations that send the measure to equivalent one. Limit points of $GL(\infty)$ can be regarded as 'spreading' maps…
Motivated by recent results regarding the equivalence of the Dirichlet and Neumann problems for the Laplace operator in the case of simply connected regions, the present paper takes a step further and provides a similar equivalence between…
This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.
One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as…
We review recent progress in operator algebraic approach to conformal quantum field theory. Our emphasis is on use of representation theory in classification theory. This is based on a series of joint works with R. Longo.
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
Some results on fixed points related to the contractive compositions of bounded operators in complete metric spaces are discussed through the manuscript. The class of composite operators under study can include, in particular, sequences of…
I review the equivalence between duality operators on two-forms and conformal structures in four dimensions, from a Clifford algebra point of view (due to Urbantke and Harnett). I also review an application, which leads to a set of…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…
We exhibit two relation algebra atom structures such that they are elementarily equivalent but their term algebras are not. This answers Problem 14.19 in the book Hirsch, R. and Hodkinson, I., "Relation Algebras by Games", North-Holland,…
We transcribe a portion of the theory of extensions of C*-algebras to general operator algebras. We also include several new general facts about approximately unital ideals in operator algebras and the C*-algebras which they generate.