Related papers: Noncommutative Superspace, Supermatrix and Lowest …
We discuss an extension of the Weingarten formula, to the case of noncommutative homogeneous spaces, under suitable "easiness" assumptions. The spaces that we consider are noncommutative algebraic manifolds, generalizing the spaces of type…
The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…
A model of the Bannai-Ito algebra in a superspace is introduced. It is obtained from the three-fold tensor product of the basic realization of the Lie superalgebra $osp(1|2)$ in terms of operators in one continuous and one Grassmanian…
In this paper we study the moduli space of 4-dimensional complex associative algebras. We use extensions to compute the moduli space, and then give a decomposition of this moduli space into strata consisting of complex projective orbifolds,…
We study identities of Lie superalgebras over a field of characteristic zero. We construct a series of examples of finite-dimensional solvable Lie superalgebras with a non-nilpotent commutator subalgebra for which PI-exponent of codimension…
In this paper we discuss a Landau levels problem within the framework of noncommutative configuration space and phase space. We show that the associated energy levels are being shifted in terms of the noncommutative parameter and can be…
We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…
We classify indefinite simply connected hyper-Kaehler symmetric spaces. Any such space without flat factor has commutative holonomy group and signature (4m,4m). We establish a natural 1-1 correspondence between simply connected…
In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional…
Let $\mathfrak A$ be a type 1 subdiagonal algebra in a $\sigma$-finite von Neumann algebra $\mathcal M$ with respect to a faithful normal conditional expectation $\Phi$. We consider a Riesz type factorization theorem in noncommutative $H^p$…
The relativistic $D=4$ Snyder model is formulated in terms of $D=4$ $dS$ algebra $o(4,1)$ generators, with noncommutative Lorentz-invariant Snyder quantum space-time provided by $\frac{O(4,1)}{O(3,1)}$ coset generators. Analogously, in…
The complete classification of classical $r$-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincar\'e groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists…
We prove the following noncommutative version of Lewis's classical result. Every n-dimensional subspace E of Lp(M) (1<p<\infty) for a von Neumann algebra M satisfies d_{cb}(E, RC^n_{p'}) \leq c_p n^{\abs{1/2-1/p}} for some constant c_p…
Massive arbitrary spin supermultiplets and massless (scalar and spin one-half) supermultiplets of the N=2 Poincare superalgebra in three-dimensional flat space are considered. Both the integer spin and half-integer spin supermultiplets are…
In this paper, by considering two non-isospectral problems with matrices chosen on the color Lie algebra $\mathfrak{sp}_{1}(6)$, we construct (1+1)-dimensional and (2+1)-dimensional super integrable systems on $\mathfrak{sp}_{1}(6)$.…
A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $\mathcal{N}=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical…
Inspired by the commutator and anticommutator algebras derived from algebras graded by groups, we introduce noncommutatively graded algebras. We generalize various classical graded results to the noncommutatively graded situation concerning…
We study N=2 superconformal theories on Euclidean and Lorentzian four-manifolds with a view toward applications to holography and localization. The conditions for supersymmetry are equivalent to a set of differential constraints including a…
In this paper, we discuss elliptic genera of (2,2) and (0,2) supersymmetric Landau-Ginzburg models over nontrivial spaces, i.e., nonlinear sigma models on nontrivial noncompact manifolds with superpotential, generalizing old computations in…
In this paper, we first introduce a quantum $n$-space with a cocommutative Hopf algebra structure. Then it is shown that to this quantum $n$-space there corresponds a derivation algebra of $\sigma$-twisted derivations related to some…