Related papers: A basis for the Birman-Wenzl algebra
In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads to so-called rack bialgebra. We construct canon-ical rack bialgebras (some kind of enveloping algebras) for any Leibniz algebra. Our motivation…
As an associative algebra, the Heisenberg-Weyl algebra $\mathcal{H}$ is generated by two elements $A$, $B$ subject to the relation $AB-BA=1$. As a Lie algebra, however, where the usual commutator serves as Lie bracket, the elements $A$ and…
We consider algebras over a field K, generated by two variables x and y subject to the single relation yx = qxy + ax + by + c for q in K^* and a, b, c in K. We prove, that among such algebras there are precisely five isomorphism classes.…
The survey is devoted to associative $\Z_{\ge0}$-graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). We consider examples of such algebras…
In this work we introduce the concept of Modular Framization or simply Framization. We construct a framization $F_{d,n}$ of the Birman--Wenzl--Murakami algebra, also known as BMW algebra, and start a systematic study of this framization. We…
The isomorphism problem means to decide if two given finite-dimensional simple algebras over the same centre are isomorphic and, if so, to construct an isomorphism between them. A solution to this problem has applications in computational…
A method to construct a geometric structure with the same solutions as a given variational principle is presented. The method applies to large families of variational principles. In particular, the known results that assign cosymplectic…
The classical characteristic map associates symmetric functions to characters of the symmetric groups. There are two natural analogues of this map involving the Brauer algebra. The first of them relies on the action of the orthogonal or…
An action of Z^l by automorphisms of a k-graph induces an action of Z^l by automorphisms of the corresponding k-graph C*-algebra. We show how to construct a (k+l)-graph whose C*-algebra coincides with the crossed product of the original…
Calder\'on-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new approach for general measure spaces which admit a Markov…
Given an algebra A, presented by generators and relations, i.e. as a quotient of a tensor algebra by an ideal, we construct a free algebra resolution of A, i.e. a differential graded algebra which is quasi-isomorphic to A and which is…
We use the Hecke algebras of affine symmetric groups and their associated Schur algebras to construct a new algebra through a basis, and a set of generators and explicit multiplication formulas of basis elements by generators. We prove that…
By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra $L(\Lambda)$ generated by indecomposable constructible sets in the varieties of modules for any finite dimensional $\mathbb{C}$-algebra $\Lambda.$ We…
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection…
Bell and Zhang have shown that if $A$ and $B$ are two connected graded algebras finitely generated in degree one that are isomorphic as ungraded algebras, then they are isomorphic as graded algebras. We exploit this result to solve the…
In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we…
Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known…
In the theory of C*-algebras, interesting noncommutative structures arise as deformations of the tensor product. For instance, the rotation algebra may be seen as a scalar twist deformation of the tensor product of the functions on the…
We begin by defining Temperley-Lieb algebra, in two different ways: as a presented algebra or as a diagrammatic algebra. Next, we look for a basis algorithmically, using rewriting theory. Finally, we introduce a generalization of the…
For a set theoretical solution of the Yang-Baxter equation $(X,\sigma)$, we define a d.g. bialgebra $B=B(X,\sigma)$, containing the semigroup algebra $A=k\{X\}/\langle xy=zt : \sigma(x,y)=(z,t)\rangle$, such that $k\otimes_A B\otimes_Ak$…