Related papers: Affine Noetherian algebras, filtrations and presen…
We prove a highest weight theorem classifying irerducible finite--dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.
Small and Zelmanov posed the question whether every element of a graded algebra over an uncountable field must be nilpotent, provided that the homogeneous elements are nilpotent. This question has recently been answered in the negative by…
A complete classification and character formulas for finite-dimensional irreducible representations of the rational Cherednik algebra of type A is given. Less complete results for other types are obtained. Links to the geometry of affine…
In this note we prove that every non characteristically filiform Lie algebra is endowed with an affine structure.
We introduce "neutrabelian algebras", and prove that finite, hereditarily neutrabelian algebras with a cube term are dualizable.
The Brylinski-Kostant filtration on a representation of a finite-dimensional semisimple Lie algebra has interpretations in terms of the algebra, geometry and combinatorics of the representation. Its extension to affine Lie algebras was…
This paper continues math.GR/0608302's study of amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and applies it to graded algebras associated with finitely generated groups. Due to a…
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 work is part of the overarching question of whether it is possible for the universal enveloping algebra of an infinite-dimensional Lie algebra to be noetherian. The main result of this paper is that the universal enveloping algebra of…
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…
We present a conjecture on the irreducibility of the tensor products of fundamental representations of quantized affine algebras. This conjecture implies in particular that the irreducibility of the tensor products of fundamental…
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…
This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated…
We treat the $\tau$-tilting finiteness of those minimal representation-infinite (min-rep-infinite) algebras which are non-distributive. Building upon the new results of Bongartz, we fully determine which algebras in this family are…
We show that a class of nonrelativistic algebras including non centrally-extended Schrodinger algebra and Galilean Conformal Algebra (GCA) has an affine extension in 2+1 hitherto unknown. This extension arises out of the conformal…
We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give…
For every finitary set functor F we demonstrate that free algebras carry a canonical partial order. In case F is bicontinuous, we prove that the cpo obtained as the conservative completion of the free algebra is the free completely…
It is shown that over an arbitrary countable field, there exists a finitely generated algebra that is nil, infinite dimensional, and has Gelfand-Kirillov dimension at most three.
We construct a nil algebra over a countable field which has finite but non-zero Gelfand-Kirillov dimension.
In this note we classify the non-Noetherian generalized Heisenberg algebras H(f) introduced by Rencai L\"u and Kaiming Zhao [Linear Algebra Appl., 2015]. In case the polynomial f has degree greater than 1, we determine all locally finite…