Related papers: An Algebraic Study of Averaging Operators
The notion of an F-manifold algebra is the underlying algebraic structure of an $F$-manifold. We introduce the notion of pre-Lie formal deformations of commutative associative algebras and show that F-manifold algebras are the corresponding…
A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the…
We consider pairs of operators $A,B\in B(H)$, where $H$ is a Hilbert space, such that there exist a linear isometry $f$ from the span of $\{A,B\}$ into $\mathbb{C}^2$ mapping $A,B$ into orthonormal vectors. We prove some necessary…
A Lax operator algebra is constructed for an arbitrary semi-simple Lie algebra over $\mathbb C$ equipped with a $\mathbb Z$-grading, and arbitrary compact Riemann surface with marked points. In this set-up, a treatment of almost graded…
We study the action of the inertia operator on the motivic Hall algebra, and prove that it is diagonalizable. This leads to a filtration of the Hall algebra, whose associated graded algebra is commutative. In particular, the degree 1…
Starting from the definition of A-Fredholm and semi-A-Fredholm operator on the standard module over a unital C*- algebra A, introduced in [8] and [4], we construct various generalizations of these operators and obtain several results as an…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
The notion of $\mathcal{O}$-operators on modules over Lie algebras generalize Rota-Baxter operators. They also generalize Poisson structures on Lie algebras in the presence of modules. Motivated from Poisson structures, we define gauge…
In the present article we define and investigate relative Rota--Baxter operators and relative averaging operators on racks and rack algebras. Also, if B is a Rota--Baxter or averaging operator on a rack X, then we can extend B by linearity…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.
Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold…
Given an automorphism and an anti-automorphism of a semigroup of a Geometric Algebra, then for each element of the semigroup a (generalized) projection operator exists that is defined on the entire Geometric Algebra. A single fundamental…
We give an analogue for vertex operator algebras and superalgebras of the notion of endomorphism ring of a vector space by means of a notion of ``local system of vertex operators'' for a (super) vector space. We first prove that any local…
The study of Reynolds algebras has its origin in the well-known work of O. Reynolds on fluid dynamics in 1895 and has since found broad applications. It also has close relationship with important linear operators such as algebra…
Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…
In this paper, first we construct two subcategories (using symmetric representations and antisymmetric representations) of the category of relative Rota-Baxter operators on Leibniz algebras, and establish the relations with the categories…
We find sufficient conditions for the construction of vertex algebraic intertwining operators, among generalized Verma modules for an affine Lie algebra $\hat{\mathfrak{g}}$, from $\mathfrak{g}$-module homomorphisms. When…
If $\fg$ is a semisimple Lie algebra, we describe the prime factors of $\mcU(\fg)$ that have enough finite dimensional modules. The proof depends on some combinatorial facts about the Weyl group which may be of independent interest. We also…
Loday introduced di-associative algebras and tri-associative algebras motivated by periodicity phenomena in algebraic $K$-theory. The purpose of this paper is to study the splittings of operations of di-associative algebras and…
We construct a one-parameter family of algebras consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of this class of operators. The operator algebra is defined by the decay…