Related papers: Semiflat Orbifold Projections

Let $G=QD_{8k}~$ be the quasi-dihedral group of order $8n$ and $\theta$ be an automorphism of $QD_{8k}$ of finite order. The fixed-point set $H$ of $\theta$ is defined as $H_{\theta}=G^{\theta}=\{x\in G \mid \theta(x)=x\}$ and generalized…

For a closed manifold equipped with a Riemannian metric, a triangulation, a representation of its fundamental group on an Hilbert module of finite type (over of finite von Neumann algebra), and a Hermitian structure on the flat bundle…

An orthogonal involution $\sigma$ on a central simple algebra $A$, after scalar extension to the function field $\mathcal{F}(A)$ of the Severi--Brauer variety of $A$, is adjoint to a quadratic form $q_\sigma$ over $\mathcal{F}(A)$, which is…

Using suitable convex functions, we construct a new family of flat Minkowski planes whose automorphism groups are at least $3$-dimensional. These planes admit groups of automorphisms isomorphic to the direct product of $\mathbb{R}$ and the…

We construct a $13$-dimensional affine variety $\mathscr{H}_{\mathbb{A}}^{13}$ associated with $\mathbb{P}^{2}\times\mathbb{P}^{2}$-fibrations of relative Picard number $1$. The construction is modelled on the fact that the affine cone over…

Drinfeld orbifold algebras are a type of deformation of skew group algebras generalizing graded Hecke algebras of interest in representation theory, algebraic combinatorics, and noncommutative geometry. In this article, we classify all…

Let $L$ be the function field of a projective space ${\mathbb P}^n_k$ over an algebraically closed field $k$ of characteristic zero, and $H$ be the group of projective transformations. An $H$-sheaf ${\mathcal V}$ on ${\mathbb P}^n_k$ is a…

Let $\gg$ be a simple, finite-dimensional complex Lie algebra, and let $V^k(\gg)$ denote the universal affine vertex algebra associated to $\gg$ at level $k$. The Cartan involution on $\gg$ lifts to an involution on $V^k(\gg)$, and we…

The aim of this thesis is to construct new examples of compact orbifolds $\mathcal{O}^4(\Theta)$ which admit a self dual Einstein (SDE) metric of positive scalar curvature $s>0$, with a one-dimensional group of isometries. In particular we…

We study the isometry groups of compact spherical orientable $3$-orbifolds $S^3/G$, where $G$ is a finite subgroup of $\mathrm{SO}(4)$, by determining their isomorphism type. Moreover, we prove that the inclusion of $\mbox{Isom}(S^3/G)$…

For every imprimitive complex reflection group of rank 2, we construct a semi-orthogonal decomposition of the derived category of the associated global quotient stack which categorifies the usual decomposition of the orbifold cohomology…

For homogeneous reductive spaces G/H with reductive complements decomposable into an orthogonal sum \mathfrak{m}=\mathfrak{m}_1 \oplus \mathfrak{m}_2 \oplus \mathfrak{m}_3 of three Ad(H)-invariant irreducible mutually inequivalent…

We construct the vortex Floer homology group $VHF (M,\mu;H)$ for an aspherical Hamiltonian $G$-manifold $(M, \omega)$ with moment map $\mu$ and a class of $G$-invariant Hamiltonian loop $H_t$, following the proposal of [3]. This is a…

We consider the group $\mathrm{Aut}(T)$ of isometries of a semi-homogeneous tree $T=T_{q_+,q_-}$ with valencies $q_+ +1$ and $q_- +1$ and its two orbits $V_+$, $V_-$ respectively. We make use of the action of $\mathrm{Aut} (T)$ to equip the…

We initiate a study of projections and modules over a noncommutative cylinder, a simple example of a noncompact noncommutative manifold. Since its algebraic structure turns out to have many similarities with the noncommutative torus, one…

Let $k$ be a commutative ring, $H$ a faithfully flat Hopf algebra with bijective antipode, $A$ a $k$-flat right $H$-comodule algebra. We investigate when a relative Hopf module is projective over the subring of coinvariants $B=A^{{\rm…

We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space $V$, and with…

Let $V$ be a vertex operator superalgebra and $g=\left(1\ 2\ \cdots k\right)$ be a $k$-cycle which is viewed as an automorphism of the tensor product vertex operator superalgebra $V^{\otimes k}$. In this paper, we construct an explicit…

The automorphism group $\Sigma$ of a compact topological projective plane with a $16$-dimensional point space is a locally compact group. If the dimension of $\Sigma$ is at least $29$, then $\Sigma$ is known to be a Lie group. For the…

Chiral orbifold models are defined as gauge field theories with a finite gauge group $\Gamma$. We start with a conformal current algebra A associated with a connected compact Lie group G and a negative definite integral invariant bilinear…