Related papers: The prime and primitive spectra of multiparameter …

The basic combinatorial properties of a complete set of mutually unbiased bases (MUBs) of a q-dimensional Hilbert space H\_q, q = p^r with p being a prime and r a positive integer, are shown to be qualitatively mimicked by the configuration…

One-parameter analogs of the Heisenberg enveloping algebra were studied previously by Kirkman and Small. In particular, they demonstrated how one may obtain Hayashi's analog of the Weyl algebra as a primitive factor of this algebra. We…

The Heisenberg double $D_q(E_2)$ of the quantum Euclidean group $\mathcal{O}_q(E_2)$ is the smash product of $\mathcal{O}_q(E_2)$ with its Hopf dual $U_q(\mathfrak{e}_2)$. For the algebra $D_q(E_2)$, explicit descriptions of its prime,…

Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in…

A framework is developed to describe the Zariski topologies on the prime and primitive spectra of a quantum algebra $A$ in terms of the (known) topologies on strata of these spaces and maps between the collections of closed sets of…

We describe the main algebraic and geometric properties of the class of algebras introduced in [arXiv:0705.1629]. We discuss their origins in symplectic geometry and associative algebra, and the notions of cohomology and representations. We…

We study the primitive recursive analogue of computable categoricity spectra for various natural classes of structures. We show that these notions coincide for all relatively $\Delta_{2}^{0}$-categorical equivalence structures and linear…

We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This…

We consider two different quantizations of the character variety consisting of all representations of surface groups in SL_2. One is the skein algebra considered by Przytycki-Sikora and Turaev. The other is the quantum Teichmuller space…

In view of a well-known theorem of Dixmier, its is natural to consider primitive quotients of $U_q^+(\mathfrak{g})$ as quantum analogues of Weyl algebras. In this work, we study these primitive quotients in the $G_2$ case and compute their…

Primes in the two complete associative normed division algebras C and H have affinities with structures seen in the standard model of particle physics. On the integers in the two algebras, there are two equivalence relations: a strong one,…

Let ${\mathfrak g}$ be a finite dimensional complex simple Lie algebra, and let $r,s\in \mathbb{C}^{\ast}$ be transcendental over $\mathbb{Q}$ such that $r^{m}s^{n}=1$ implies $m=n=0$. We will obtain some basic properties of the…

Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…

The simple symplectic triple systems over the real numbers are classified up to isomorphism, and linear models of all of them are provided. Besides the split cases, one for each complex simple Lie algebra, there are two kinds of non-split…

To each simple Lie algebra g and an element w of the corresponding Weyl group De Concini, Kac and Procesi associated a subalgebra U^w_- of the quantized universal enveloping algebra U_q(g), which is a deformation of the universal enveloping…

This paper is devoted to study of differential calculi over quadratic algebras, which arise in the theory of quantum bounded symmetric domains. We prove that in the quantum case dimensions of the homogeneous components of the graded vector…

text of abstract (We present a utilitarian review of the family of matrix groups $Sp(2n,\Re)$, in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more…

We give a systematic construction of Hopf algebra structures on braided cofree coalgebras. The relevant underlying structures are braided algebras and braided coalgebras. We provide some interesting examples of these algebras and coalgebras…

We give integral presentations of quantum lattice Heisenberg algebras by viewing them as Heisenberg doubles. Our presentations generalize those appearing previously in the literature.

We analyse the algebras generated by free component quantum fields together with the susy generators $Q,\bar Q$. Restricting to hermitian fields we first construct the scalar field algebra from which various scalar superfields can be…