Related papers: Stated skein algebras and their representations
We survey various constructions of finite dimensional projective representations of mapping class groups derived from stated skein algebras.
We construct finite-dimensional projective representations of the mapping class groups of compact connected oriented surfaces having one boundary component using stated skein algebras.
The stated skein algebra is a generalization of the Kauffman bracket skein algebra introduced in the study of quantum trace maps. When the quantum parameter is a root of unity, the stated skein algebra has a big center and is finitely…
Skein algebras of surfaces quantize character varieties of topological surfaces, and in low genus, these quantizations are often related to algebras arising in representation theory. For example, Terwilliger defined a universal $SL_2$…
We give an explicit correspondence between stated skein algebras, which are defined via explicit relations on stated tangles in [Costantino F., L\^e T.T.Q., arXiv:1907.11400], and internal skein algebras, which are defined as internal…
This is a survey on extended affine Lie algebras and related types of Lie algebras, which generalize affine Lie algebras.
This is a survey paper on Alegbraic Geometry over Lie Algebras
We study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is isomorphic to the quantum group ${\mathcal O}_{q^2}(\mathrm{SL}(2))$ providing a…
We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.
This article is a comprehensive review of the representation theory of the Ariki-Koike algebras and the cyclotomic Schur algebras.
We classify the finite dimensional semi-weight representations of the reduced stated skein algebras at odd roots of unity of connected marked surfaces which either have a boundary component with at least two boundary edges or which do not…
We give generators and relations for the planar algebras corresponding to $ADE$ subfactors. We also give a basis and an algorithm to express an arbitrary diagram as a linear combination of these basis diagrams.
We provide finite presentations for stated skein algebras and deduce that those algebras are Koszul and that they are isomorphic to the quantum moduli algebras appearing in lattice gauge field theory, generalizing previous results of…
The input and output algebras of an infinite qubit system and their representations are described.
The classification of the representations of the generalized deformed oscillator algebra is given together with several comments about possibility of introducing a coproduct structure in some type of deformed oscillator algebra.
Given a graph E we define E-algebraic branching systems, show their existence and how they induce representations of the associated Leavitt path algebra. We also give sufficient conditions to guarantee faithfulness of the representations…
This paper defines several algebras associated to an oriented surface $S$ with a finite set of marked points on the boundary. The first is the skein algebra $Sk_q(S)$, which is spanned by links in the surface which are allowed to have…