Related papers: Two parameter deformation of Grassmann matrix grou…
The Gauss decomposition of quantum groups and supergroups are considered. The main attention is paid to the R-matrix formulation of the Gauss decomposition and its properties as well as its relation to the contraction procedure. Duality…
We propose a new structure ${\cal U}^{r}_{\displaystyle{q}}(sl(2)) $. This is realized by multiplying $\delta$ ($q=e^{\delta}$, $\delta\in \CC$) by $\theta$, where $\theta$ is a real nilpotent -paragrassmannian- variable of order $r$…
Representation theory for the Jordanian quantum algebra U=U_h(sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators of U on the basis…
We obtain the basic $R$-matrix of the two-parameter Quantum group $U=U_{r,s}\mathcal(\mathfrak{so}_{2n})$ via its weight representation theory and determine its $R$-matrix with spectral parameters for the two-parameter quantum affine…
We introduce the h-deformation of the algebra of functions on the grassmann supergroup Gr$(1|1)$ via a contraction of Gr$_q(1|1)$.
We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are…
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on R^2 taking values in a Grassmann algebra with N generating elements are described up to an equivalence transformation for N \ne 2.
We study dualities of the general Galileon theory in d dimensions in terms of coordinate transformations on the coset space corresponding to the spontaneously broken Galileon group. The most general duality transformation is found to be…
We deform two-dimensional topological gravity by making use of its gauge theory formulation. The obtained noncommutative gravity model is shown to be invariant under a class of transformations that reduce to standard diffeomorphisms once…
Some special solutions of the Einstein-Maxwell action with a non-negative cosmological constant and a very heavy point mass particle have been obtained. The solutions correspond to static spacetime of locally constant curvature in its…
We examine a recently proposed class of integrable deformations to two-dimensional conformal field theories. These {\lambda}-deformations interpolate between a WZW model and the non-Abelian T-dual of a Principal Chiral Model on a group G…
In this paper, we introduce non-standard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces denoted by ${\mathbb A}_h^{1|2}$ and ${\mathbb A}_{h'}^{2|1}$,…
We characterise the quantum group gauge symmetries underlying q-deformations of two-dimensional Yang-Mills theory by studying their relationships with the matrix models that appear in Chern-Simons theory and six-dimensional N=2 gauge…
We derive the master function governing the component action of the four-dimensional non-anticommutative (NAC) and fully N=2 supersymmetric gauge field theory with a non-simple gauge group U(2)=SU(2)xU(1). We use a Lorentz singlet…
Paragrassmann algebras with one and many paragrassmann variables are considered from the algebraic point of view without using the Green ansatz. Operators of differentiation with respect to paragrassmann variables and a covariant…
We provide a Faddeev-Reshetikhin-Takhtajan's RTT approach to the quantum group Fun(GL_{r,s}(n)) and the quantum enveloping algebra U_{r,s}(gl_n) corresponding to the two-parameter R-matrix. We prove that the quantum determinant det_{r,s}T…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
We discuss two-parameter deformations of an universal enveloping algebra $U(g[u])$ of a polynomial loop algebra $g[u]$, where $g$ is a finite-dimensional complex simple Lie algebra (or superalgebra). These deformations are Hopf algebras.…
Schemes based on anticommuting scalar coordinates, corresponding to properties, lead to generations of particles naturally. The application of Grassmannian duality cuts down the number of states substantially and is vital for constructing…
We study a suitable q-deformed version of the Moriya's superexchange interaction theory by means of its underlying quantum group structure. We show that the one-dimensional chain case is associated with the non-standard quantum group…