Related papers: Commuting signs of infinity

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

Lie-Yamaguti algebras (or generalized Lie triple systems) are binary-ternary algebras intimately related to reductive homogeneous spaces. The Lie-Yamaguti algebras which are irreducible as modules over their Lie inner derivation algebra are…

We consider two algebras of curves associated to an oriented surface of finite type - the cluster algebra from combinatorial algebra, and the skein algebra from quantum topology. We focus on generalizations of cluster algebras and…

The K\"ahler-Yang-Mills equations are coupled equations for a K\"ahler metric on a compact complex manifold and a connection on a complex vector bundle over it. After briefly reviewing the main aspects of the geometry of the…

We introduce C-Algebras of compact Riemann surfaces $\Sigma$ as non-commutative analogues of the Poisson algebra of smooth functions on $\Sigma$. Representations of these algebras give rise to sequences of matrix-algebras for which…

This text provides an introduction and complements to some basic constructions and results in 2-representation theory of Kac-Moody algebras.

Supersymmetric field theories on noncommutative spaces are constructed. We present two different representations of noncommutative space, but we can obtain supersymmetry algebla and supersymmetric Yang-Mills action independent of its…

This is a short note on the relation of the Matrix model with the non-commutative geometry of the 11-dimensional supermembrane. We put forward the idea that M-theory is described by the 't Hooft topological expansion of the Matrix model in…

We explore maximally supersymmetric Yang-Mills theory with walls of impurities respecting half of the supersymmetries. The walls carry fundamental or bifundamental matter multiplets. We employ three-dimensional N=2 superspace language to…

Yang-Mills gauge theory models on a cylinder coupled to external matter charges provide powerful means to find and solve certain non-linear integrable systems. We show that, depending on the choice of gauge group and matter charges, such a…

We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasi-Yang-Baxter algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and…

We propose $N=2$ holomorphic Yang-Mills theory on compact K\"{a}hler manifolds and show that there exists a simple mapping from the $N=2$ topological Yang-Mills theory. It follows that intersection parings on the moduli space of…

Both boundary maps in K-theory are expressed in terms of surjections from projective C*-algebras to semiprojective C*-algebras.

Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $\Sigma_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by…

This essay's title is justified by discussing a class of Yang-Mills-type theories of which standard Yang-Mills theories are special cases but which is broad enough to include gravity as a double field theory. We use the framework of…

We consider the extension of classical 2-dimensional topological quantum field theories to Klein topological quantum field theories which allow unorientable surfaces. We approach this using the theory of modular operads by introducing a new…

A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang-Mills theory is constructed and used to examine some generic properties of noncommutative quantum…

We construct symmetries of the Chalmers-Siegel action describing self-dual Yang-Mills theory using a canonical transformation to a free theory. The symmetries form an infinite dimensional Lie algebra in the group algebra of isometries.

Inspired by the Weierstrass representation of smooth affine minimal surfaces with indefinite metric, we propose a constructive process producing a large class of discrete surfaces that we call discrete affine minimal surfaces. We show that…

Recently, a new generalized family of infinite-dimensional $ \widetilde{W} $ algebras, each associated with a particular element of a commutative subalgebra of the $ W_{1+\infty} $ algebra, was described. This paper provides a comprehensive…