Related papers: Symmetric quantum Weyl algebras
We classify reflexive graded right ideals, up to isomorphism and shift, of generic cubic three dimensional Artin-Schelter regular algebras. We also determine the possible Hilbert functions of these ideals. These results are obtained by…
We classify right coideal subalgebras of the finite-dimensional quotient of the quantized enveloping algebra $U_q(\mathfrak{sl}_2)$ and that of the quantized coordinate algebra $\mathcal{O}_q(SL_2)$ at a root of unity $q$ of odd order. All…
Quantum algebras U_q(su_n) used as the algebras of flavour symmetry (usually described by SU(n)) to study static properties of hadrons lead to intriguing results. In this contribution we focus on the peculiar properties manifested by…
On any Reflection Equation algebra corresponding to a skew-invertible Hecke symmetry (i.e. a special type solution of the Quantum Yang-Baxter Equation) we define analogs of the partial derivatives. Together with elements of the initial…
We formulate a $q$-Schur algebra associated to an arbitrary $W$-invariant finite set $X_{\texttt f}$ of integral weights for a complex simple Lie algebra with Weyl group $W$. We establish a $q$-Schur duality between the $q$-Schur algebra…
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in $h$. They are derived from the quantized enveloping algebras $\uqg$. The quantum Lie bracket satisfies a generalization of antisymmetry.…
A quantized symplectic oscillator algebra of rank 1 is a PBW deformation of the smash product of the quantum plane with U_q(sl_2). We study its representation theory, and in particular, its category O.
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
The Weyl algebra (W_{2m}[h]; *) is the algebra generated by u=(u_1,...,u_m,v_1,.....,v_m) over C with the fundamental commutation relation [u_i,v_j]=-ih\delta_{ij}, where h is a positive constant. The Heisenberg algebra (\Cal H_{2m}[nu];*)…
The main result of this work is to present the complete list of Uq(sl2)-symmetries of quantum plane. For that, the structure of quantum plane automorphisms is used. Our idea in classifying the above symmetries is in introducing some special…
Let $S$ be a spinor bundle of a pseudo-Euclidean vector bundle $(E,\mathrm{g})$ of even rank. We introduce a new filtration on the algebra $\mathcal{D}(M,S)$ of differential operators on $S$. As main property, the associated graded algebra…
We define two subalgebras which can be seen as the quantization of the coordinate rings of the unipotent radical of the standard positive (respectively negative) Borel subgroup of $SL_{n+1}$. We give a presentation for these algebras and…
It is believed that any classical gauge symmetry gives rise to an L$_\infty$ algebra. Based on the recently realized relation between classical ${\cal W}$ algebras and L$_\infty$ algebras, we analyze how this generalizes to the quantum…
In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form…
We obtain Schur-Weyl dualities in which the algebras, acting on both sides, are semigroup algebras of various symmetric inverse semigroups and their deformations.
We introduce Weyl n-algebras and show how their factorization homology may be used to define invariants of manifolds. In the appendix we heuristically explain why these invariants must be perturbative Chern-Simons invariants.
We study the space of biinvariants and zonal spherical functions associated to quantum symmetric pairs in the maximally split case. Under the obvious restriction map, the space of biinvariants is proved isomorphic to the Weyl group…
For the case of quantum loop algebras $\mathrm U_q(\mathcal L(\mathfrak{sl}_{l + 1}))$ with $l = 1, 2$ we find the $\ell$-weights and the corresponding $\ell$-weight vectors for the representations obtained via Jimbo's homomorphism, known…
In this paper, the module-algebra structures of $U_q(sl(m+1))$ on the quantum $n$-space $A_q(n)$ are studied. We characterize all module-algebra structures of $U_q(sl(m+1))$ on $A_q(2)$ and $A_q(3)$ when $m\geq 2$. The module-algebra…
Various applications of quantum algebraic techniques in nuclear and molecular physics are briefly reviewed. Emphasis is put in the study of the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies,…