Related papers: Stated skein algebras and their representations
The aim of this note is to give a gentle introduction to algebras of partial triangulations of marked surfaces, following the structure of a talk given during the 49th symposium on ring theory and representation theory, held in Osaka. This…
The concept of a crossed tensor product of algebras is studied from a few points of views. Some related constructions are considered. Crossed enveloping algebras and their representations are discussed. Applications to the noncommutative…
In this thesis, we explore the representation theory of double affine Hecke algebras (DAHAs) through the lens of stated skein theory. Over the past decade, there have been several works establishing robust connections between skein algebras…
This is an expository article on diagrammatic representations of knots and links in various settings via braids.
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting…
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 identify…
Pseudoalgebras, introduced in [BDK], are multi-dimensional analogues of conformal algebras, which provide an axiomatic description of the singular part of the operator product expansion. Our main interest in this paper is the pseudoalgebra…
We give an explicit presentation for the Kauffman bracket skein algebra of the $5$-punctured sphere over any commutative unitary ring.
We present some old and new results on dispersive estimates for Schroedinger equations.
We prove that both stated skein algebras and their reduced versions at odd roots of unity are almost-Azumaya and compute the rank of a reduced stated skein algebra over its center, extending a theorem of Frohman, Kania-Bartoszynska and L\^e…
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible…
Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced…
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
Survey article on representation stability and examples in algebraic geometry and topology, written for the Notices of the AMS.
This paper presents an overview of the current state of knowledge in the field of equivariant map algebras and discusses some open problems in this area.
This paper is the third in a series of papers, the aim of which is to construct algebraic geometry over metabelian Lie algebras.
This is a survey on coarse geometry with an emphasis on coarse homology theories.
This paper describes finite dimensionall irreducible representations of both twisted and untwisted Cartan map Lie superalgebras.
A model of representations of a Lie algebra is a representation which a direct sum of all irreducible finite dimensional representations taken with multiplicity $1$. In the paper an explicit construction of a model of representation for all…
According to Letourmy and Vendramin, a representation of a skew brace is a pair of representations on the same vector space, one for the additive group and the other for the multiplicative group, that satisfies a certain compatibility…