We propose a graphic method to derive the classical algebra (Dirac brackets) of non-local conserved charges in the two-dimensional supersymmetric non-linear O(N) sigma model. As in the purely bosonic theory we find a cubic Yangian algebra. We also consider the extension of graphic methods to other integrable theories. 1 Introduction Non-linear sigma models [1-3] are prototypes of a remarkable c...

For G a locally compact group and G its dual, let Jd(G) be the C*algebra generated by the Fourier-Stieltjes transforms of the discrete measures on G. We show that the canonical trace on ,4(G) is faithful if and only if G is amenable as a discrete group. We further show that if G is nondiscrete and amenable as a discrete group, then the only measures in dKd(G) are the discrete measures, and also...

1 Describing measurable sets 8 1.1 Families of sets . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.1 Semiring of sets . . . . . . . . . . . . . . . . . . . . . . 9 1.1.2 Restricted algebras . . . . . . . . . . . . . . . . . . . . 12 1.1.3 Sigma Algebras . . . . . . . . . . . . . . . . . . . . . . 12 1.1.4 Binary Unions . . . . . . . . . . . . . . . . . . . . . . 14 1.1.5 Initial Sigm...

abstract The Virasoro master equation describes a large set of conformal field theories known as the affine-Virasoro constructions, in the operator algebra (affine Lie algebra) of the WZW model, while the Einstein equations of the general non-linear sigma model describe another large set of conformal field theories. This talk summarizes recent work which unifies these two sets of conformal fiel...

counterpart , these new observables in A∈A ( ) ′′ A A ω π A have no abstract counterpart in . However, they will have an abstract counterpart in . There is also a natural embedding of A into ∗∗ ∗∗ ∗∗ ⊆ A A A such that . The most common way to construct a von Neumann algebra is to start with a C*-algebra and an abstract state A ω , construct a representation ( , ω ) π ω π H ( via the GNS theorem...

We consider the algebra $\dot\Sigma(\mathcal L)$ generated by inner-limit derivations over ${\rm GICAR}$ of a fermion gas populating an aperiodic Delone set $\mathcal L$. Under standard physical assumptions such as finite interaction range, Galilean invariance and continuity with respect to lattice, we demonstrate that image $\dot \Sigma(\mathcal through Fock representation can be completed gro...

Abstract We present here a multiplicative version of the classical Kowalski–Słodkowski theorem, which identifies characters among collection all functionals on complex and unital Banach algebra A . In particular, we show that, if is $C^\star $ -algebra, $\phi :A\to \mathbb C continuous function satisfying \phi (x)\phi (y) \in \sigma (xy) for $x,y\in A$ (where $\sigma denotes spectrum), then eit...