相关论文: What is a vertex algebra?

This is an informal write up of my talk in Berlin. It gives some background to Goddard's talk (math.QA/9808136) about the moonshine conjectures.

Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of…

We give a description of the connected graded algebras which are finitely generated and presented of global dimension 2 or 3 and which are Gorenstein. These algebras are constructed from multilinear forms. We generalize the construction by…

We consider some bases in the Hecke algebra and exhibit certain dualities between them.

We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and set theoretical viewpoints.

Let $V$ be a vertex algebra and $M$ a $V$-module. We define the first and second cohomology of $V$ with coefficients in $M$, and we show that the second cohomology $H^{2}(V, M)$ corresponds bijectively to the set of equivalence classes of…

We construct an example of an $A_{\infty}$ algebra structure defined over a finite dimensional graded vector space.

A complete classification of two-dimensional algebras over algebraically closed fields is provided

This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…

Notes on Commutative Alegbra and Algebraic Geometry covering rings, ideals, modules, presheaves, sheaves, schemes, homological algebra, \'etale cohomology and further topics that are more advanced.

A synaptic algebra is a generalization of the Jordan algebra of selfadjoint elements of a von Neumann algebra. We study symmetries in synaptic algebras, i.e., elements whose square is the unit element, and we investigate the equivalence…

Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras $\Theta.$ For every algebra $H$ in $\Theta$ one can consider algebraic geometry in $\Theta$ over $ H.$ Correspondingly, algebras in…

All subalgebras, idempotents, left(right) ideals and left quasi-units of two-dimensional algebras are described. Classification of algebras with given number of subalgebras, left(right) ideals are provided. In particular, a list of…

A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.

We study the connectedness and the diameter of orthogonality graphs of upper triangular matrix algebras over arbitrary fields.

The purpose of this note is to establish an isomorphism from the vector space of extensions between two modules over a vertex algebra, to an appropriate first chiral homology of one dimensional projective space with coefficients in the…

This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…

These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.

The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…

The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.