相关论文: A geometric proof of the classification of complex…
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are…
The aim of this paper is to give an alternative proof of Kac's theorem for weighted projective lines (\cite{W}) over the complex field. The geometric realization of complex Lie algebras arising from derived categories (\cite{XXZ}) is…
This is a continuation of the authors' previous work [math.AT/9910001] on classification of equivariant complex vector bundles over a circle. In this paper we classify equivariant real vector bundles over a circle with a compact Lie group…
In this paper we characterize the fiber representations of equivariant complex vector bundles over a circle and classify these bundles. We also treat the triviality of equivariant complex vector bundles over a circle by investigating the…
We introduce a construction of highly arc transitive digraphs using a layerwise direct product. This product generalizes some known classes of highly arc transitive digraphs but also allows to construct new such. We use the product to…
We outline a proof of the categorical geometric Langlands conjecture for GL(2), as formulated in reference [AG], modulo a number of more tractable statements that we call Quasi-Theorems.
For an elliptic curve $E$ defined over the field $\mathbb{C}$ of complex numbers, we classify all translates of elliptic curves in $E^3$ such that the $x$-coordinates satisfy a linear equation. This classification enables us to establish a…
Beginning from the resolution of the Dirichlet L function, using the inner product formula between two infinite-dimensional vectors in the complex space, the author proved the baffling problem--Hecke conjecture.
A surprising simple result about quadrilaterals is given as an application of the vector triple product identity.
We prove the Categorified Wrapping Number Conjecture for large classes of annular links, including alternating annular links and tangle closures exhibiting plumbed link phenomena. We do so by characterizing when a resolution is sufficient…
The category of crossed complexes gives an algebraic model of the category of $CW$-complexes and cellular maps. We explain basic results on crossed complexes which allow the computation of free crossed resolutions of graph products of…
We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are…
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
A brief proof of Lie's classification of finite dimensional subalgebras of vector fields on the complex plane that have a proper Levi decomposition is given. The proof uses basic representation theory of sl(2, C). This, combined with…
We present a geometric interpretation of tight closure in terms of vector bundles and projective bundles.
We introduce lexicographic cones, a method of assigning an ordered vector space $\Lex(S)$ to a poset $S$, generalising the standard lexicographic cone. These lexicographic cones are then used to prove that the projective tensor cone of two…
We present a new proof of the classification of complex simple Lie algebras via the projective geometry of homogeneous varieties. Our proof proceeds by constructing homogeneous varieties using the ideals of the secant and tangential…
Let $R\subseteq E$ be two Lie conformal algebras and $Q$ be a given complement of $R$ in $E$. Classifying complements problem asks for describing and classifying all complements of $R$ in $E$ up to an isomorphism. It is known that $E$ is…
A graded tensor category over a group $G$ will be called a crossed product tensor category if every homogeneous component has at least one multiplicatively invertible object. Our main result is a description of the crossed product tensor…
A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.