Related papers: Subtraction Menger algebras
Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…
In this paper we study some fundamental algebraic properties of slice functions and slice regular functions over an alternative $^*$-algebra $A$ over $\mathbb{R}$. These recently introduced function theories generalize to higher dimensions…
In recent years, the study of slice monogenic functions has attracted more and more attention in the literature. In this paper, an extension of the well-known Dirac operator is defined which allows to establish the Lie superalgebra…
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.
We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R.…
We introduce the notion of the partial group algebra with projections and relations and show that this C*-algebra is a partial crossed product. Examples of partial group algebras with projections and relations are the Cuntz-Krieger algebras…
Very recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced to unify the theory of monogenic functions and of slice monogenic functions over Clifford algebras. Inspired by the work of A.…
We construct the field A generated by n algebraically independent elements, and show that the linear space of derivations over this field is faithfully represented by the linear space of the n-th fold Cartesian product of this field acting…
We study star product algebras of analytic functions for which the power series defining the products converge absolutely. Such algebras arise naturally in deformation quantization theory and in noncommutative quantum field theory. We…
New index transforms are investigated, which contain as the kernel products of the Bessel and modified Bessel functions. Mapping properties and invertibility in Lebesgue spaces are studied for these operators. Relationships with the…
We construct a family of subalgebras of the Gerstenhaber algebra of differential operators. The subalgebras are labeled by subsets of the additive group ${\mathbb Z}^n$ that are closed under addition. Each subalgebra is invariant under the…
Contragenic functions are defined to be reduced-quaternion-valued harmonic functions which are orthogonal to all monogenic and antimonogenic functions in the $L^2$ norm of a given domain. The parallelism between the spaces of contragenic…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to…
We investigate the problem whether a given multiplier of a tensor product of two algebras belongs to the tensor product of multiplier algebras. We give a characterization of such multipliers in the case when one of the algebras is the…
We present complete classifications of automorphisms of two closed subalgebras of the bounded analytic functions on the open unit disc $\mathbb{D}$, namely, the subalgebra of functions vanishing at the origin, and the subalgebra of…
This paper introduces a new subtraction operation for convex sets, which defines their difference as a collection of inclusion-minimal convex sets with appropriate definitions of linear operations on them. With these operations the set of…
We consider various collections of functions from the Baire space X into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings,…
Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…
Let $\langle K,\nu \rangle$ be a real closed valued field, and let $S\subseteq K^n$ be an open semi-algebraic set. Using tools from model theory, we find an algebraic characterization of rational functions which admit, on $S$, only values…