Related papers: Depth of Boolean algebras

We study the size blow-up that is necessary to convert an algebraic circuit of product-depth $\Delta+1$ to one of product-depth $\Delta$ in the multilinear setting. We show that for every positive $\Delta = \Delta(n) = o(\log n/\log \log…

We give sufficient conditions on planar domains for polynomials to be dense in the algebras A and A-infinity of the product of these domains, endowed with their natural topologies. We also characterize the uniform limits, with respect to…

We extend the result of arXiv:0911.5414 about embedding of ideal-determined algebraic systems into ultraproducts, to arbitrary algebraic systems, and to ultraproducts over $\kappa$-complete ultrafilters. We also discuss the scope of…

We prove an analog of the disintegration theorem for tracial von Neumann algebras in the setting of elementary equivalence rather than isomorphism, showing that elementary equivalence of two direct integrals implies fiberwise elementary…

We study a family of dissections of flow polytopes arising from the subdivision algebra. To each dissection of a flow polytope, we associate a polynomial, called the left-degree polynomial, which we show is invariant of the dissection…

A notion of support for objects in any Grothendieck category is introduced. This is based on the spectral category of a Grothendieck category and uses its Boolean lattice of localising subcategories. The support provides a classification of…

We generalize Bourgain's discretized sum-product theorem to matrix algebras.

A general deformation theory of algebras which factorise into two subalgebras is studied. It is shown that the classification of deformations is related to the cohomology of a certain double complex reminiscent of the Gerstenhaber-Schack…

This article is devoted to showing the product theorem for Bowen's topological entropy.

The regular open subsets of a topological space form a Boolean algebra, where the `join' of two regular open sets is the interior of the closure of their union. A `credence' is a finitely additive probability measure on this Boolean…

Depth of an object concerns a tradeoff between computation time and excess of program length over the shortest program length required to obtain the object. It gives an unconditional lower bound on the computation time from a given program…

We introduce the Lie algebra of super-operators associated with a quantum filter, specifically emerging from the Stratonovich calculus. In classical filtering, the analogue algebra leads to a geometric theory of nonlinear filtering which…

Ultrafilters are very useful and versatile objects with applications throughout mathematics: in topology, analysis, combinarotics, model theory, and even theory of social choice. Proofs based on ultrafilters tend to be shorter and more…

We establish a correspondence between the levels of Verlinde rings and the depths of subfactors. Given the $l$-level Verlinde ring $R_l(G)$ of a simple compact Lie group $G$, the tensor products of fundamental representations give us the…

We continue algebraization of the set of ultrafilters on a metric spaces initiated in [6]. In particular, we define and study metric counterparts of prime, strongly prime and right cancellable ultrafilters from the Stone-$\check{C}$ech…

The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…

Let $M_n$ be a sequence of finite factors with $\dim(M_n)\rightarrow \infty$ and denote $\text{\bf M}=\Pi_\omega M_n$ their ultraproduct over a free ultrafilter $\omega$. We prove that if $\text{\bf Q}\subset \text{\bf M}$ is either an…

Let K denote a field. Given an arbitrary linear subspace V of M_n(K) of codimension lesser than n-1, a classical result states that V generates the K-algebra M_n(K). Here, we strengthen this in three ways: we show that M_n(K) is spanned by…

It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extend this is still true. We give an explicit description of the…

We consider several distinct characterizations of finite implication algebras. One of these leads to a new characterization of Boolean polymatroids.