Let $\Sigma$ be a finite type surface, and $G$ complex algebraic simple Lie group with algebra $\mathfrak{g}$. The quantum moduli of $(\Sigma,G)$ is quantization the ring functions $X_G(\Sigma)$, variety $G$-characters $\pi_1(\Sigma)$, introduced by Alekseev-Grosse-Schomerus Buffenoir-Roche in mid '90s. It can realized as invariant subalgebra so-called graph algebras, which are $U_q(\mathfrak{g...

We describe an $E_k$-cell structure on the free $E_{k+1}$-algebra a point, and more generally how May-Milgram filtration of $\Omega^m \Sigma^m S^{k}$ lifts to $E_{k+m}$-algebra point by iterated pushouts $E_k$-algebras.

We define a nonassociative generalization of cyclic Azumaya algebras employing skew polynomial rings $D[t;\sigma]$, where $D$ is an algebra constant rank with center $C$ and $\sigma$ automorphism $D$, such that $\sigma|_{C}$ has finite order. The automorphisms these are canonically induced by ring the $D[t;\sigma]$ used in their construction. achieve description inner automorphisms. Results on ...

Effective actions are derived for (2,0) and (2,1) superstrings by studying the corresponding sigma-models. The geometry is a generalisation of Kahler geometry involving torsion and the field equations imply that the curvature with torsion is self-dual in four dimensions, or has SU(n, m) holonomy in other dimensions. The Yang-Mills fields are self-dual in four dimensions and satisfy a form of th...

In 1996 Goulden and Jackson introduced a family of coefficients $( c_{\pi, \sigma}^{\lambda} ) $ indexed by triples partitions which arise in the power sum expansion some Cauchy for Jack symmetric functions $(J^{(\alpha )}_\pi )$. The can be viewed as an interpolation between structure constants class algebra double coset algebra. suggested that are polynomials variable $\beta := \alpha-1$ with...

The first-order formulation of the principal sigma model with a Lie group target space is performed. By using the dualisation of the algebra and the field content of the theory the field equations which are solely written in terms of the field strengths are realized through an extended symmetry algebra parametrization. The structure of this symmetry algebra is derived so that it generates the r...

We prove that the dualization algebra of the symmetric space coset sigma model is a Lie algebra and we show that it generates an appropriate adjoint representation which enables the local integration of the field equations yielding the first-order ones.

The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.

On a supersymmetric sigma model the covariantly constant forms are related to the conserved currents that are generators of a super W-algebra extending the superconformal algebra. The existence of covariantly constant forms restricts the holonomy group of the manifold. Via duality transformation we get new covariantly constant forms, thus restricting the holonomy group of the new manifold. e-ma...