Related papers: Combinatorial classification of $(\pm 1)$-skew pro…

In this paper we study deformation classes of moduli spaces of sheaves on a projective K3 surface. More precisely, let $(S1,H1)$ and $(S2,H2)$ be two polarized K3 surfaces, $m\in\mathbb{N}$, and for $i=1,2$ let $mv_{i}$ be a Mukai vector on…

When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is…

In this note, we prove that the invariant subalgebra of the (-1)-skew polynomial algebra under a permutation action is a graded isolated singularity, and thus a conjecture of Chan-Young-Zhang is true.

We study the deformation theory of projective Stanley-Reisner schemes associated to combinatorial manifolds. We achieve detailed descriptions of first order deformations and obstruction spaces. Versal base spaces are given for certain…

We study the six-dimensional pseudo-Riemannian spaces with two time-like coordinates that admit non-homothetic infinitesimal projective transformations. The metrics are manifestly obtained and the projective group properties are determined.…

Real index pairings of projections and unitaries on a separable Hilbert space with a real structure are defined when the projections and unitaries fulfill symmetry relations invoking the real structure, namely projections can be real,…

We study Van den Bergh's noncommutative symmetric algebra $\mathbb{S}^{nc}(M)$ (over division rings) via Minamoto's theory of Fano algebras. In particular, we show $\mathbb{S}^{nc}(M)$ is coherent, and its proj category $\mathbb{P}^{nc}(M)$…

In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…

In 2010, B. Rhoades proved that promotion together with the fake-degree polynomial associated with rectangular standard Young tableaux give an instance of the cyclic sieving phenomenon. We extend this result to all skew standard Young…

The "projective lightcone limit" has been proposed as an alternative holographic dual of an AdS space. It is a new type of group contraction for a coset G/H preserving the isometry group G but changing H. In contrast to the usual group…

String diagrams can nicely express numerous computations in symmetric strict monoidal categories (SSMC). To be entirely exact, this is only true for props: the SSMCs whose monoid of objects are free. In this paper, we show a propification…

We show that the superconformal symmetries of the (1,1) sigma model decompose into a set of more refined symmetries when the target space admits projectors $P_{\pm}$, and the orthogonal complements $Q_{\pm}$, covariantly constant with…

For any rank-one Riemannian symmetric space S of non-compact type and any discrete, cofinite, non-cocompact, torsion-free group $\Gamma$ of orientation-preserving Riemannian isometries on S, we develop a cohomological interpretation for the…

We give a unifying description of all inequivalent vector bundles over the 2-dimensional sphere $S^2$ by constructing suitable global projectors $p$ via equivariant maps. Each projector determines the projective module of finite type of…

The representations of dimension vector $\alpha$ of the quiver Q can be parametrised by a vector space $R(Q,\alpha)$ on which an algebraic group $\Gl(\alpha)$ acts so that the set of orbits is bijective with the set of isomorphism classes…

In this paper, we study a generalization of the notion of AS-regularity for connected $\mathbb{Z}$-algebras. Our main result is a characterization of those categories equivalent to noncommutative projective schemes associated to right…

Here, a non-linear analysis method is applied rather than classical one to study projective Finsler geometry. More intuitively, by means of an inequality on Ricci-Finsler curvature, a projectively invariant pseudo-distance is introduced and…

We introduce computable projection operators onto piecewise polynomial spaces, defined via sampling and discrete least-squares polynomial approximations. The resulting mappings exhibit (almost) optimal approximation properties in $L^2$ and…

Positive Quaternion Kaehler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. We prove this conjecture in dimension 20 under additional…

A quantum solvable algebra is an iterated $q$-skew extension of a commutative algebra. We get finite statification of prime spectrum for quantum solvable algebras obeying some natural conditions. We prove that for any prime ideal $I$ the…