Related papers: Operadic semi-infinite homology
Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…
In two seminal papers M. Kontsevich introduced graph homology as a tool to compute the homology of three infinite dimensional Lie algebras, associated to the three operads `commutative,' `associative' and `Lie.' We generalize his theorem to…
The symmetric inverse semigroup $I(X)$ on a set $X$ is the collection of all partial bijections between subsets of $X$ with composition as the algebraic operation. We study a minimal Hausdorff inverse semigroup topologies on $I(X)$. When…
Many finite symmetric integral non-representable relation algebras, including almost all Monk algebras, can be embedded in the completion of an atomic symmetric integral representable relation algebra whose finitely-generated subalgebras…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…
In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras
The goal of this paper is to set up an obstruction theory in the context of algebras over an operad and in the framework of differential graded modules over a field. Precisely, the problem we consider is the following: Suppose given two…
This paper surveys recent work on Lie algebras of differential operators and their application to the construction of quasi-exactly solvable Schroedinger operators.
We provide a very general approach to placing model structures and semi-model structures on algebras over symmetric colored operads. Our results require minimal hypotheses on the underlying model category $\mathcal{M}$, and these hypotheses…
We consider various homological operations on homology of quandles. We introduce the notion of quandle partial derivatives, and extreme chains on which appropriate partial derivatives vanish. Extreme chains yield homological operations. We…
In this paper we study a natural extension of Kontsevich's characteristic class construction for A-infinity and L-infinity algebras to the case of curved algebras. These define homology classes on a variant of his graph homology which…
We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence…
The notion of double coset for semisimple finite dimensional Hopf algebras is introduced. This is done by considering an equivalence relation on the set of irreducible characters of the dual Hopf algebra. As an application formulae for the…
For a restricted Lie algebra $L$, the conditions under which its restricted enveloping algebra $u(L)$ is semiperfect are investigated. Moreover, it is proved that $u(L)$ is left (or right) perfect if and only if $L$ is finite-dimensional.
We give a new and conceptually straightforward proof of the well-known presentation for the Temperley-Lieb algebra, via an alternative new presentation. Our method involves twisted semigroup algebras, and we make use of two apparently new…
This paper studies averaging algebras, say, associative algebras endowed with averaging operators. We develop a cohomology theory for averaging algebras and justify it by interpreting lower degree cohomology groups as formal deformations…
We introduce the semi-infinite category of sheaves on the affine Grassmannian, and construct a particular object in it, which we call the the semi-infinite intersection cohomology sheaf. We relate it to several other entities naturally…
We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.
Several quantum systems have been used in the last few years to extend supersymmetry. In this paper we show all this systems fit into the picture of what we call "Number Operator Algebras".
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.