Related papers: Properadic coformality of spheres

We introduce quantum super-spherical pairs as coideal subalgebras in general linear and orthosymplectic quantum supergroups. These subalgebras play a role of isotropy subgroups for matrices solving $\mathbb{Z}_2$-graded reflection equation.…

Inspired by the simple fact that a compact n-dimensional manifold-with-boundary which satisfies Poincar\'e-Lefschetz duality of dimension n has a boundary which itself satisfies Poincar\'e duality of dimension n, we show that the…

Since the time when the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way to formalize it in mathematics is…

We study actions of ``compact quantum groups'' on ``finite quantum spaces''. According to Woronowicz and to general $\c^*$-algebra philosophy these correspond to certain coactions $v:A\to A\otimes H$. Here $A$ is a finite dimensional…

The universal $2$-parameter vertex algebra $\mathcal{W}_{\infty}$ of type $\mathcal{W}(2,3,\dots)$ is a classifying object for vertex algebras of type $\mathcal{W}(2,3,\dots,N)$ for some $N$; under mild hypotheses, all such vertex algebras…

In this paper we take some classical ideas from commutative algebra, mostly ideas involving duality, and apply them in algebraic topology. To accomplish this we interpret properties of ordinary commutative rings in such a way that they can…

We describe the E-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its…

We define a basic class of algebras which we call homotopy path algebras. We find that such algebras always admit a cellular resolution and detail the intimate relationship between these algebras, stratifications of topological spaces, and…

We describe a kind of deformation of the anti-DeRham algebra on a Calabi-Yau manifold $X$. These are in 1-1 correspondence with the total cohomology $\oplus H^i (X, \C)$.

We study a class of quantized enveloping algebras, called twisted Yangians, associated with the symmetric pairs of types B, C, D in Cartan's classification. These algebras can be regarded as coideal subalgebras of the extended Yangian for…

Let $R$ be a ring with unity and $\mathcal{X}$ a semibrick in the module category $\mathrm{Mod}\,R$, that is, a class of pairwise orthogonal finitely presented modules whose endomorphism rings are division rings. We study the full…

To each complex number $\lambda$ is associated a representation $\pi_\lambda$ of the conformal group $SO_0(1,n)$ on $\mathcal C^\infty(S^{n-1})$ (spherical principal series). For three values $\lambda_1,\lambda_2,\lambda_3$, we construct a…

Any Batalin-Vilkovisky algebra with a homotopy trivialization of the BV-operator gives rise to a hypercommutative algebra structure at the cochain level which, in general, contains more homotopical information than the hypercommutative…

E. Cartan proved that conformally flat hypersurfaces in S^{n+1} for n>3 have at most two distinct principal curvatures and locally envelop a one-parameter family of (n-1)-spheres. We prove that the Gauss-Codazzi equation for conformally…

There has been a long-standing question about whether being perfectoid for an algebra is local in the analytic topology. We provide affirmative answers for the algebras (e.g., over $\overline{\mathbb{Z}_p}$) whose spectra are inverse limits…

Let X be a Calabi-Yau threefold and \mu the symmetric trilinear form on the second cohomology group H^{2}(X,\Z) defined by the cup product. We investigate the interplay between the Chern classes c_{2}(X), c_{3}(X) and the trilinear form…

We define holomorphic structures on canonical line bundles of the quantum projective space $\qp^{\ell}_q$ and identify their space of holomorphic sections. This determines the quantum homogeneous coordinate ring of the quantum projective…

We show that pairs $(X,Y)$ of 1-spherical objects in $A_\infty$-categories, such that the morphism space ${\rm Hom}(X,Y)$ is concentrated in degree 0, can be described by certain noncommutative orders over (possibly stacky) curves. In fact,…

In this paper we will introduce a new notion of geometric structures defined by systems of closed differential forms in term of the Clifford algebra of the direct sum of the tangent bundle and the cotangent bundle on a manifold. We develop…

Let $Y$ be a compact Gorenstein analytic space with only isolated singularities and trivial dualizing sheaf. A recent paper of Imagi studies the deformation theory of $Y$ in case the singularities of $Y$ are weighted homogeneous and…