Related papers: Stated skein algebras and their representations

We consider a construction of the fundamental spin representations of the simple Lie algebras $\mathfrak{so}(n)$ in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a…

This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.

We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra $\mathscr{S}_{\Sigma,\mathbb{W}}^{A}$ of a walled surface $(\Sigma,\mathbb{W})$, and prove that it has a quantum…

In the present paper we generalize the notion of a Heyting algebra to the non-commutative setting and hence introduce what we believe to be the proper notion of the implication in skew lattices. We list several examples of skew Heyting…

We describe presentations of the Roger-Yang generalized skein algebras for punctured spheres with an arbitrary number of punctures. This skein algebra is a quantization of the decorated Teichmuller space and generalizes the construction of…

This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…

This paper surveys the representation theory of rational Cherednik algebras. We also discuss the representations of the spherical subalgebras. We describe in particular the results on category O. For type A, we explain relations with the…

Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.

In this paper we introduce the notion of twisted symplectic reflection algebras and describe the category of representations of such an algebra associated to a non-faithful G-action in terms of those for faithful actions of G.

There is a connection between *-representations of algebras associated with graphs and the problem about the spectrum of a sum of Hermitian operators (spectral problem). For algebras associated with extended Dynkin graphs we give an…

This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low…

The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…

This is a survey talk on the study of Gel'fand-Dorfman bialgebras.

In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.

We consider two algebras of curves associated to an oriented surface of finite type - the cluster algebra from combinatorial algebra, and the skein algebra from quantum topology. We focus on generalizations of cluster algebras and…

In the paper, we show some properties of (reduced) stated $\mathrm{SL}(n)$-skein algebras related to their centers for essentially bordered pb surfaces, especially their centers, finitely generation over their centers, and their PI-degrees.…

Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $\Sigma_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by…

The higher-spin (HS) algebras so far known can be interpreted as the symmetries of the minimal representation of the isometry algebra. After discussing this connection briefly, we generalize this concept to any classical Lie algebras and…

A class of well-behaved *-representations of a q-deformed Heisenberg algebra is studied and classified.

In this paper we study the representation theory for certain ``half lattice vertex algebras.'' In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these…