Related papers: Noncommutative Superspace, Supermatrix and Lowest …
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.
Let $\mathfrak{r}$ be a finite dimensional complex Lie superalgebra with a non-degenerate super-symmetric invariant bilinear form, let $\mathfrak{p}$ be a finite dimensional complex super vector space with a non-degenerate super-symmetric…
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant…
This is a noncommutative-geometric study of the semiclassical dynamics of finite topological D-brane systems. Starting from the formulation in terms of A -infinity categories, I show that such systems can be described by the noncommutative…
We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This…
We consider quantum mechanics on the noncommutative spaces characterized by the commutation relations $$ [x_a, x_b] \ =\ i\theta f_{abc} x_c\,, $$ where $f_{abc}$ are the structure constants of a Lie algebra. We note that this problem can…
In a previous paper [M.~Hanada, H.~Kawai and Y.~Kimura, Prog. Theor. Phys. 114 (2005), 1295] it is shown that a covariant derivative on any n-dimensional Riemannian manifold can be expressed in terms of a set of n matrices, and a new…
In this article, we construct some examples of noncommutative projective Calabi-Yau schemes by using noncommutative Segre products and quantum weighted hypersurfaces. We also compare them with commutative Calabi-Yau varieties and examples…
Working in the geometric approach, we construct the lagrangians of N=1 and N=2 pure supergravity in four dimensions with negative cosmological constant, in the presence of a non trivial boundary of space-time. We find that the supersymmetry…
We construct the mirror algebra to a smooth affine log Calabi-Yau variety with maximal boundary, as the spectrum of a commutative associative algebra with a canonical basis, whose structure constants are given as naive counts of…
We construct three-dimensional non-semisimple topological field theories from the unrolled quantum group of the Lie superalgebra $\mathfrak{osp}(1 \vert 2)$. More precisely, the quantum group depends on a root of unity $q=e^{\frac{2 \pi…
Let L be a Lie group and Lambda a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L, and the image of G on L/Lambda is dense. Let c be a diagonalizable element of G not contained in a compact…
We show that the noncommutative spheres of Connes and Landi are quantum homogeneous spaces for certain compact quantum groups. We give a general construction of homogeneous spaces which support noncommutative spin geometries.
We give necessary conditions for the existence of a compact manifold locally modelled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and…
Suppose the ground field $\mathbb{F}$ is an algebraically closed field characteristic of $p>2$. In this paper, we investigate the restricted cohomology theory of restricted Lie superalgebras. Algebraic interpretations of low dimensional…
We consider 4d $\mathcal{N}=1$ supergravity theories with modular symmetry, where the modulus $\tau$ is the upper half-plane modulo $SL(2,\mathbf{Z})$ action. We focus on enhanced discrete gauge symmetry points $\tau=i, \exp(2\pi i/3)$, and…
A way to construct (conjecturally all) simple finite dimensional modular Lie (super)algebras over algebraically closed fields of characteristic not 2 is offered. In characteristic 2, the method is supposed to give only simple Lie…
We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the $UOSp(2\vert 1)$ supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already…
In this contribution we present a general procedure that allows the construction of noncommutative spaces with quantum group invariance as the quantization of their associated coisotropic Poisson homogeneous spaces coming from a coboundary…
By direct calculations of matrix form of super Jacobi and mixed super Jacobi identities which are obtained from adjoint representation, and using the automorphism supergroup of the gl(1|1) Lie superalgebra, we determine and classify all…