Related papers: An operator algebra associated with a pair of inte…
An elliptic theory is constructed for operators acting in subspaces defined via odd pseudodifferential projections. Subspaces of this type arise as Calderon subspaces for first order elliptic differential operators on manifolds with…
The notion of vertex operator coalgebra is presented and motivated via the geometry of conformal field theory. Specifically, we describe the category of geometric vertex operator coalgebras, whose objects have comultiplicative structures…
There exists two types of nonassociative algebras whose associator satisfies a symmetric relation associated with a 1-dimensional invariant vector space with respect to the natural action of the symmetric group on three elements. The first…
We show that every operator system (and hence every unital operator algebra) has sufficiently many boundary representations to generate the C*-envelope.
A pseudodifferential calculus for parameter-dependent operators on smooth manifolds with boundary in the spirit of Boutet de Monvel's algebra is constructed. The calculus contains, in particular, the resolvents of realizations of…
We review the notion of submanifold algebra, as introduced by T. Masson, and discuss some properties and examples. A submanifold algebra of an associative algebra $A$ is a quotient algebra $B$ such that all derivations of $B$ can be lifted…
Clifford geometric algebras of multivectors are treated in detail. These algebras are build over a graded space and exhibit a grading or multivector structure. The careful study of the endomorphisms of this space makes it clear, that…
A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a…
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
Given a manifold with boundary endowed with an action of a discrete group on it, we consider the algebra of operators generated by elements in the Boutet de Monvel algebra of pseudodifferential boundary value problems and shift operators…
We define a class of deformed multimode oscillator algebras which possess number operators and can be mapped to multimode Bose algebra.We construct and discuss the states in the Fock space and the corresponding number operators.
This paper mainly concerns the von Neumann algebras induced by a tuple of multiplication operators on Bergman spaces which arise essentially from holomorphic proper maps over higher dimensional domains. We study the structures and abelian…
We show that any multiplicative bijection between the algebras of differentiable functions, defined on differentiable manifolds of positive dimension, is an algebra isomorphism, given by composition with a unique diffeomorphism.
Diassociative algebras form a categoy of algebras recently introduced by Loday. A diassociative algebra is a vector space endowed with two associative binary operations satisfying some very natural relations. Any diassociative algebra is an…
A Rodrigues type formula is obtained for the symbols of the covariant bi-differential operators on a simple Jordan algebra.
We give a short direct proof of Agler's factorization theorem that uses the abstract characterization of operator algebras. the key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional…
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
We introduce a notion of an algebra of generalized pseudo-differential operators and prove that a spectral triple is regular if and only if it admits an algebra of generalized pseudo-differential operators. We also provide a self-contained…