Related papers: Stated skein algebras and their representations
General braided counterparts of classical Clifford algebras are introduced and investigated. Braided Clifford algebras are defined as Chevalley-Kahler deformations of the corresponding braided exterior algebras. Analogs of the spinor…
We obtain a presentation of Schur algebras (and q-Schur algebras) by generators and relations which is compatible with the usual presentation of the enveloping algebra (quantized enveloping algebra) corresponding to the Lie algebra gl(n) of…
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
The paper studies the structure of restricted Leibniz algebras. More specifically speaking, we first give the equivalent definition of restricted Leibniz algebras, which is by far more tractable than that of a restricted Leibniz algebras in…
This survey is intended as an invitation to the theory of stable $\infty$-categories, addressed primarily to mathematicians working in the representation theory of algebras and related subjects.
We establish a lower bound for the representation dimension of all the classical Hecke algebras of types A, B and D. For all the type A algebras, and most of the algebras of types B and D, we also establish upper bounds. Moreover, we…
This paper introduces an algebra structure on the part of the skein module of an arbitrary $3$-manifold $M$ spanned by links that represent $0$ in $H_1(M;\mathbb{Z}_2)$ when the value of the parameter used in the Kauffman bracket skein…
Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfect matchings of a snake graph. In this paper, we continue our…
This survey paper aims at giving the state of the art in the study of string C-group representations of almost simple groups. It also suggest a series of problems and conjectures to the interested reader.
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
We use evaluation representations to give a complete classification of the finite-dimensional simple modules of twisted current algebras. This generalizes and unifies recent work on multiloop algebras, current algebras, equivariant map…
A knot invariant is called skein if it is determined by a finite number of skein relations. In the paper we discuss some basic properties of skein invariants and mention some known examples of skein invariants.
Representations of CCR algebras in spaces of entire functions are classified on the basis of isomorphisms between the Heisenberg CCR algebra A_H and star algebras of holomorphic operators. To each representations of such algebras,…
This is an expository article on representation theory of toroidal Lie algebras. We summerize all the results on representation theory of toroidal Lie algebras obtained in the last fifteen years. Apart from that a natural genaralization of…
A general framework for obtaining certain types of contracted and centrally extended algebras is presented. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models.
This article gives a summary of the finite-dimesional irreducible representations of the $q$-Onsager algebra, which are treated in detail in our paper `The augmented tridiagonal algebra'.
The present paper is devoted to the description of finite-dimensional semisimple Leibniz algebras over complex numbers, their derivations and automorphisms.
We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.
We study a physically motivated representation of an algebra of operators in gravitational and non gravitational theories called the covariant representation of an algebra. This is a representation where the symmetries of the operator…