相关论文: Razborov flag algebras as algebras of measurable f…

We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…

\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are…

Using functional equations, we define functors that generalize standard examples from calculus of one variable. Examples of such functors are discussed and their Taylor towers are computed. We also show that these functors factor through…

In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…

We consider affine representable algebras, that is, finitely generated algebras over a field that can be embedded into some matrix algebra over a commutative algebra. We show that this algebra can in fact be chosen to be a polynomial…

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real…

A compact T-algebra is an initial T-algebra whose inverse is a final T-coalgebra. Functors with this property are said to be algebraically compact. This is a very strong property used in programming semantics which allows one to interpret…

We characterize the non-commutative Aleksandrov--Clark measures and the minimal realization formulas of contractive and, in particular, isometric non-commutative rational multipliers of the Fock space. Here, the full Fock space over…

We develop the theory of categories of measurable fields of Hilbert spaces and bounded fields of bounded operators. We examine classes of functors and natural transformations with good measure theoretic properties, providing in the end a…

We propose the Lie-algebraic interpretation of poly-analytic functions in $L_2(\C,d\mu)$, with the Gaussian measure $d\mu$, based on a flag structure formed by the representation spaces of the $\mathfrak{sl}(2)$-algebra realized by…

Using Grothendieck's "functor of points" approach to algebraic geometry, we define a new infinite-dimensional algebro-geometric flag space as a $k$-functor (for $k$ a ring) which maps a $k$-algebra $R$ to the set of certain well-ordered…

We study irreducible *-representations of a certain quantization of the algebra of polynomial functions on a generalized flag manifold regarded as a real manifold. All irreducible *-representations are classified for a subclass of flag…

For a semi-simple simply connected algebraic group G we introduce certain parabolic analogues of the Nekrasov partition function (introduced by Nekrasov and studied recently by Nekrasov-Okounkov and Nakajima-Yoshioka for G=SL(n)). These…

We introduce a new family of symmetric functions, which are $q$-analogues of products of Schur functions defined in terms of ribbon tableaux. These functions can be interpreted in terms of the Fock space representation of the quantum affine…

This is part II of our book on KAM theory. We start by defining functorial analysis and then switch to the particular case of Kolmogorov spaces. We develop functional calculus based on the notion of local operators. This allows to define…

On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…

This paper defines for each object $X$ that can be constructed out of a finite number of vertices and cells a vector $fX$ lying in a finite dimensional vector space. This is the flag vector of $X$. It is hoped that the quantum topological…

We provide bar and cobar constructions as functors between some categories of curved algebras and curved augmented coalgebras over a graded commutative ring. These functors are adjoint to each other.

We develop a theory of minimal models for algebras over an operad defined over a commutative ring, not necessarily a field, extending and supplementing the work of Sagave in the associative case.