Related papers: Presenting cyclotomic q-Schur algebras

Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their…

Generalizing recent work of Brundan and Kleshchev, we introduce grading on Dipper-James' $q$-Schur algebra, and prove a graded analogue of the Leclerc and Thibon's conjecture on the decomposition numbers of the $q$-Schur algebra when…

In this note we study a family of algebras with one parameter defined by generators and relations. The set of generators contains the generators of the usual braids algebra, and another set of generators which is interpreted as ties between…

Our constructions provide a systematic way to study cohomology tri-dendriform algebra via classical cohomology, simplifying computations and enabling the use of established techniques.

We decompose the full and reduced C*-algebras of an extension of a groupoid by the circle into a direct sum of twisted groupoid C*-algebras.

Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…

Attention is focused on q-deformed quantum algebras with physical importance, i.e. $U_{q}(su_{2})$, $U_{q}(so_{4})$ and q-deformed Lorentz algebra. The main concern of this article is to assemble important ideas about these symmetry…

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

The finite dimensional representations of associative quadratic algebras with three generators are investigated by using a technique based on the deformed parafermionic oscillator algebra. One application on the calculation of the…

We give a new type of Schur-Weyl duality for the representations of a family of quantum subgroups and their centralizer algebra. We define and classify singly-generated, Yang-Baxter relation planar algebras. We present the skein theoretic…

To each symmetric algebra we associate a family of algebras that we call quantum affine wreath algebras. These can be viewed both as symmetric algebra deformations of affine Hecke algebras of type $A$ and as quantum deformations of affine…

An idea to present a classical Lie group of positive dimension by generators and relations sounds dubious, but happens to be fruitful. The isometry groups of classical geometries admit elegant and useful presentations by generators and…

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.

In this work, we introduce a new class of algebras called skew-Brauer graph algebras, which generalize the well-known Brauer graph algebras. We establish that skew-Brauer graph algebras are symmetric and can be defined using a Brauer graph…

We introduce a cyclotomic representation for finite $q$-hypergeometric series and $q$-deformed amplitudes that separates algebraic structure from evaluation. By expressing each summand in a sparse exponent basis over irreducible cyclotomic…

We use the representation theory of preprojective algebras to construct and study certain cluster algebras related to semisimple algebraic groups.

Let $S(\Lambda)$ be the cyclotomic q-Schur algebra associated to the Ariki-Koike algebra $H$. We construct a certain subalgebra $S^0(\Lambda)$ of $S(\Lambda)$, and show that it is a standardly based algebra in the sense of Du and Rui.…

The connection between q-analogs of special functions and representations of quantum algebras has been developed recently. It has led to advances in the theory of q-special functions that we here review.

We introduce a class of proper differential graded algebras which we call Serre cyclotomic. They generalize fractionally Calabi-Yau algebras and categorify de la Pe\~na's algebras of cyclotomic type. Path algebras of affine type and…

We show that the quantum algebra $U_q(sl_2)$ has a presentation with generators $x,x^{-1},y,z$ and relations $x x^{-1}=1$, $x^{-1} x=1$, $\frac{qxy-q^{-1}yx}{q-q^{-1}}=1$, $\frac{qyz-q^{-1}zy}{q-q^{-1}}=1$,…