相关论文: On the parallelepipeds in algebra and topology

The tangled closure of a collection of subsets of a topological space is the largest subset in which each member of the collection is dense. This operation models a logical `tangle modality' connective, of significance in finite model…

This work adapts the equivalent definitions of division algebras over a field into multiple types of division algebras in a monoidal category. Examples and consequences of these definitions are then established in various monoidal settings.

We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.

A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category of posets which are equivalent to a variety. This is quite analogous to Lawvere's classical…

We present the topological classification of real parts of real regular elliptic surfaces with a real section.

We describe a class of genus 2 closed hyperbolic 3-manifolds of arbitrarily large volume.

A generalization of incidence relations in abstract polytope has been explored, and parameterized surfaces are used as primers. The abstract orientable incidence structure is defined as an algebraic model of incidence relations, in which…

We introduce a new class of possibly noncompact n-dimensional manifolds without boundary associated to finite data which we call topological automata. This class is large enough to contain many interesting examples of open 2-dimensional and…

We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism…

We classify pointed Hopf algebras of discrete corepresentation type over an algebraically closed field K with characteristic zero. For such algebras $H$, we explicitly determine the algebra structure up to isomorphism for the link…

We classify strongly homotopy Lie algebras - also called L-infinity algebras - of one even and two odd dimensions, which are related to $2|1$-dimensional $Z_2$-graded Lie algebras. What makes this case interesting is that there are many…

We establish a parametric extension $h$-principle for overtwisted contact structures on manifolds of all dimensions, which is the direct generalization of the $3$-dimensional result from \cite{Eli89}. It implies, in particular, that any…

We study flat vector bundles over complex parallelizable manifolds.

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

We classify almost del Pezzo manifolds in arbitrary dimension n, i.e., projective manifolds X with big and nef anticanonical bundle -K_X, such that -K_X is divisible by n-1.

We obtain some restrictions on the topology of infinite volume hyperbolic manifolds. In particular, for any n and any closed negatively curved manifold M of dimension greater than 2, only finitely many hyperbolic n-manifolds are total…

Let $(M,J)$ be a $n$-dimensional complex manifold: a $p$-K\"ahler structure (resp. $p$-symplectic structure) on $M$ is a real, closed $(p,p)$-transverse form $\Omega$ (resp. real, closed $2p$-form whose $(p,p)$-component is transverse). We…

Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.

We classify the finite dimensional irreducible representations of affine Hecke algebras of type B_2 with unequal parameters.

Let k be an algebraically closed field of characteristic 0 and let D_m be the dihedral group of order 2m with m= 4t, with t bigger than 2. We classify all finite-dimensional Nichols algebras over D_m and all finite-dimensional pointed Hopf…