Related papers: Rota-type operators on 2-dimensional dendriform al…
A discriminant algebra operation sends a commutative ring $R$ and an $R$-algebra $A$ of rank $n$ to an $R$-algebra $\Delta_{A/R}$ of rank $2$ with the same discriminant bilinear form. Constructions of discriminant algebra operations have…
In this paper, we introduce and study a new class of bounded linear operators on complex Hilbert spaces, which we call 2-C-normal operators. This class is inspired by and closely related to the notion of 2-normal operators, with additional…
We give a few observations on different types of bounded operators on a topological vector space X and their relations with compact operators on X. In particular, we investigate when these bounded operators coincide with compact operators.…
A long standing problem of Gian-Carlo Rota for associative algebras is the classification of all linear operators that can be defined on them. In the 1970s, there were only a few known operators, for example, the derivative operator, the…
We consider the vector space of $n \times n$ matrices over $\mathbb C$, Fermi operators and operators constructed from these matrices and Fermi operators. The properties of these operators are studied with respect to the underlying…
We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…
In this paper, we construct Laplace-Beltrami operators associated with arbitrary Riemannian metrics on noncommutative tori of any dimension. These operators enjoy the main properties of the Laplace-Beltrami operators on ordinary Riemannian…
We describe all Rota-Baxter operators of any weight on the space of matrices from $M_2(F)$ considered under the product $a\circ b = (ab + ba)/2$ and usually denoted as $M_2(F)^{(+)}$. This algebra is known to be a simple Jordan one. We…
A Rota-Baxter algebra $A_R$ is an algebra $A$ equipped with a distinguished Rota-Baxter operator $R$ on it. Rota-Baxter algebras are closely related to dendriform algebras introduced by Loday. In this paper, we first consider the…
The goal of this work is to introduce the notion of $3$-Hom-Lie-dendriform algebras which is the dendriform version of $3$-Hom-Lie-algebras. They can be also regarded as the ternary analogous of Hom-Lie-dendriform algebras. We give the…
We describe all Rota-Baxter operators $R$ of weight zero on the matrix algebra $M_3(F)$ over a quadratically closed field $F$ of characteristic not 2 or 3 such that $R(1)\neq0$. Thus, we get a partial classification of solutions to the…
Defining conditions for irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that…
We classify all Rota-Baxter operators on the simple conformal Lie algebra $\mathrm{Cur}(\mathrm{sl}_2(\mathbb{C}))$ and clarify which of them arise from the solutions to the conformal classical Yang-Baxter equation due to the connection…
In this paper, we introduce an algebra structure denoted by InvDer algebra whose which we twist an algebra thanks to an invertible derivation, where its inverse is also a derivation. We define InvDer Lie algebras, InvDer associated…
There is a certain family of conformally invariant first order elliptic operators on Riemannian spin manifold which include Dirac operator as its first and simplest member. Their general definition is given and their basic properties are…
We show that several convolution operators on the space of entire functions, such as the MacLane operator, support a dense hypercyclic algebra that is not finitely generated. Birkhoff's operator also has this property on the space of…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
In this paper, we introduce the notion of curved $\mathcal{O}$-operator systems as a generalization of T. Brzezi\'{n}ski's (curved) Rota-Baxter systems, and then investigate their relations with $\mathcal{O}$-operator systems,…
$\mathcal{O}$-operators are important in broad areas in mathematics and physics, such as integrable systems, the classical Yang-Baxter equation, pre-Lie algebras and splitting of operads. In this paper, a deformation theory of…
A general method to easily build global and relative operators for any number n of elementary systems if they are defined for 2 is presented. It is based on properties of the morphisms valued in the tensor products of algebras of the…