Related papers: Number Operator Algebras
The algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the $q$-bracket, is a quasimodular form. More generally, if a graded algebra $A$ of functions on…
Suppose q is a complex number of modulus one and different from 1,-1. Let O(R^2_q) be the *-algebra with two hermitean generators x and y satisfying the relation xy=qyx. Using operator representations of the *-algebra O(R^2_q) on Hilbert…
In the present paper the algebras of functions on quantum homogeneous spaces are studied. The author introduces the algebras of kernels of intertwining integral operators and constructs quantum analogues of the Poisson and Radon transforms…
We construct Baxter operators for the homogeneous closed $\mathrm{XXX}$ spin chain with the quantum space carrying infinite or finite dimensional $s\ell_2$ representations. All algebraic relations of Baxter operators and transfer matrices…
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital…
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…
The field equations of the auxiliary fields are nonlinear and free of derivatives. Hence, it is argued, a Legendre transform to generate the 1PI Generating Functionals is not correct for the auxiliary fields. A corrected formulation of the…
Bosons and fermions are often written by elements of other algebras. M. Abe gave a recursive realization of the boson by formal infinite sums of the canonical generators of the Cuntz algebra ${\cal O}_{\infty}$. We show that such formal…
We use a result of Barron, Dong and Mason to give a natural isomorphism between the category of twisted modules and the category of quasi-modules of a certain type for a general vertex operator algebra.
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…
In this paper we give a detailed classification scheme for three-dimensional quantum zero curvature representation and tetrahedron equations. This scheme includes both even and odd parity components, the resulting algebras of observables…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
The quon algebra gives a description of particles, ``quons,'' that are neither fermions nor bosons. The parameter $q$ attached to a quon labels a smooth interpolation between bosons, for which $q = +1$, and fermions, for which $q = -1$.…
This article presents a natural extension of the tensor algebra. In addition to "left multiplications" by vectors, we can consider "derivations" by covectors as basic operators on this extended algebra. These two types of operators satisfy…
We discuss the notion of a Batalin-Vilkovisky (BV) algebra and give several classical examples from differential geometry and Lie theory. We introduce the notion of a quantum operator algebra (QOA) as a generalization of a classical…
Corresponding to a finite dimensional Hilbert space $H$ with $\dim H=n$, we define a geometric algebra $\gscript (H)$ with $\dim\sqbrac{\gscript (H)}=2^n$. The algebra $\gscript (H)$ is a Hilbert space that contains $H$ as a subspace. We…
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which…
We generalize to arbitrary categories of algebras the notion of an NS-algebra. We do this by using a bimodule property, as we did for defining the general notions of a dendriform and tridendriform algebra. We show that several types of…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
Nonlinear pseudo-fermions of degree n (n-pseudo-fermions) are introduced as (pseudo) particles with creation and annihilation operators $a$ and $b$, $b \neq a^\dagger$, obeying the simple nonlinear anticommutation relation $ab + b^n a^n =…