Related papers: Atomic polyadic algebras of infinite dimension are…
In this paper we study of *-representations for polynomial algebras on quantum matrix spaces. We deal with two special cases of the polynomial algebras, namely the algebra of polynomials on quantum complex matrices $\mathrm{Mat_2}$ and on…
We study the nonsymmetric Macdonald polynomials specialized at infinity from various points of view. First, we define a family of modules of the Iwahori algebra whose characters are equal to the nonsymmetric Macdonald polynomials…
The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible $*$-representations of the q-deformed algebra $U'_q(so_{2,2})$ which is a real form of the non-standard deformation…
We show that provided $n\ne 3$, the involutive Hopf *-algebra $A_u(n)$ coacting universally on an $n$-dimensional Hilbert space has enough finite-dimensional representations in the sense that every non-zero element acts non-trivially in…
Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight representations are classified, and shown to be…
We show that the big Ramsey degree of the Boolean algebra with 3 atoms within the countable atomless Boolean algebra is infinite.
We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We…
We determine the maximal dimension of totally geodesic subalgebras of N-graded filiform Lie algebras, and we show that these bounds are attained.
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 introduce "neutrabelian algebras", and prove that finite, hereditarily neutrabelian algebras with a cube term are dualizable.
Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove an inequality involving the energy and the discriminant and apply it to deduce a result on totally positive…
We study the construction of premonoidal categories, where the pentagon relation fails, through representations of finite group algebras and their quantum doubles. Both finite group algebras and their quantum doubles have a finite number of…
To a representation of $\O_N$ (the Cuntz algebra with $N$ generators) we associate a projection valued measure and we study the case when this measure has atoms. The main technical tool are the spaces invariant for all the operators…
In this note we present a more detailed and explicit exposition of the definition of a conformal representation of a Leibniz algebra. Recall (arXiv:math/0611501v3) that Leibniz algebras are exactly Lie dialgebras. The idea is based on the…
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the most general associative cubic algebra and we present specific…
We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.
It is shown that if the universal enveloping algebra of a simple $\mathbb Z^n$-graded Lie algebra is Noetherian, then the Lie algebra is finite-dimensional.
We consider an infinite dimensional generalization of Metaplectic representations (Weil representations) for the (double covering of) symplectic group. Given quasifree states of an infinite dimensional CCR algebra, projective unitary…
We establish a lower bound for the representation dimension of all the classical Hecke algebras of types A, B and D. For all the type A algebras, and most of the algebras of types B and D, we also establish upper bounds. Moreover, we…
There are 6 types of 2-dimensional representations in general. For any groups and any monoids, we can construct the moduli of 2-dimensional representations for each type: the moduli of absolutely irreducible representations, representations…