Related papers: Commuting signs of infinity
The Yangian symmetry Y(su($n$)) of the Calogero-Sutherland-Moser spin model is reconsidered. The Yangian generators are constructed from two non-commuting su($n$)-loop algebras. The latters generate an infinite dimensional symmetry algebra…
Yang-Mills gauge theory on Minkowski space supports a Batalin-Vilkovisky-infinity algebra structure, all whose operations are local. To make this work, the axioms for a BV-infinity algebra are deformed by a quadratic element, here the…
It is pointed out that despite of the non-linearity of the underlying equations, there do exist rather general methods that allow to generate new minimal surfaces from known ones.
We characterize the smallest finite spaces with the same homotopy groups of the spheres. Similarly, we describe the minimal finite models of any finite graph. We also develop new combinatorial techniques based on finite spaces to study…
It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be formulated in a $d+2$-dimensional space, with the extra two dimensions forming a surface with non-commutative geometry.
Derivations of a noncommutative algebra can be used to construct differential calculi, the so-called derivation-based differential calculi. We apply this framework to a version of the Moyal algebra ${\cal{M}}$. We show that the differential…
We relate the semiclassical limit of the quantum Yang-Mills partition function on a compact oriented surface to the symplectic volume of the moduli space of flat connections, by using an explicit expression for the symplectic form. This…
We apply the fusion procedure to a quantum Yang-Baxter algebra associated with time-discrete integrable systems, notably integrable quantum mappings. We present a general construction of higher-order quantum invariants for these systems. As…
Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding…
In this review, we present a general framework for the construction of Kac-Moody (KM) algebras associated to higher-dimensional manifolds. Starting from the classical case of loop algebras on the circle $\mathbb{S}^{1}$, we extend the…
Commuting maps on a class of algebras called inflated algebras are investigated. In particular, we can prove that every commuting map $\theta$ on such an algebra is of the form $\theta(x)=c x+\mu(x)$, where $c$ belongs to the base field $K$…
It is known that the spin structure on a Riemannian manifold can be extended to noncommutative geometry using the notion of a spectral triple. For finite geometries, the corresponding finite spectral triples are completely described in…
It is conjectured that there exist finitely many isomorphism classes of simple endomorphism algebras of abelian varieties of GL_2-type over \Q of bounded dimension. We explore this conjecture when particularized to quaternion endomorphism…
We analyze the partition function of two dimensional Yang-Mills theory on a family of surfaces of infinite genus. These surfaces have a recursive structure, which was used by one of us to compute the partition function that results in a…
This paper presents a derivation of the possible residual symmetries of rational K-matrices which are invertible in the ''classical limit'' (the spectral parameter goes to infinity). This derivation uses only the boundary Yang-Baxter…
This paper defines several algebras associated to an oriented surface $S$ with a finite set of marked points on the boundary. The first is the skein algebra $Sk_q(S)$, which is spanned by links in the surface which are allowed to have…
We define commutants mod normed ideals associated with compact smooth manifolds with boundary. The results about the K-theory of these operator algebras include an exact sequence for the connected sum of manifolds, derived from the…
On a Riemannian manifold of dimension $n$ we extend the known analytic results on Yang-Mills connections to the class of connections called $\Omega$-Yang-Mills connections, where $\Omega$ is a smooth, not necessarily closed, $(n-4)$-form.…
The status of several representative gauge theories on various quantum space-times, mainly focusing on Yang-Mills type extensions together with a few matrix model formulations is overviewed. The common building blocks are derivation based…
This is a review article in which we will introduce, in a unifying fashion and with more intermediate steps in some difficult calculations, two infinite-dimensional Lie algebras of quantum matrix models, one for the open string sector and…