相关论文: Cellularity of free products of Boolean algebras (…

We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subset A such that 2^{|A|} = 2^{|B|}. This implies in particular that B has 2^{|B|} subalgebras. We also discuss…

Let $\Lambda$ be a finite-dimensional algebra over an algebraically closed field, then $\Lambda$ is either tame or wild. Is there any homological description in terms of AR-translations on tameness? Or equivalently, is there any…

Given a partially ordered set $P$ there exists the most general Boolean algebra $F(P)$ which contains $P$ as a generating set, called the {\it free Boolean algebra} over $P$. We study free Boolean algebras over posets of the form $P=P_0\cup…

In this paper, we prove that the cyclotomic BMW algebras B2p+1,n are cellular in the sense of [16]. We also classify the irreducible B2p+1,nmodules over a field.

We prove that assuming suitable cardinal arithmetic, if B is a Boolean algebra every homomorphic image of which is isomorphic to a factor, then B has locally small density. We also prove that for an (infinite) Boolean algebra B, the number…

We investigate free products of finite dimensional $C^*$-algebras with amalgamation over diagonal subalgebras. We look to determine under what circumstances a given free product is exact and/or nuclear. In some cases we find a description…

It is proved that the free Boolean topological group $B(X)$ on a Tychonoff space $X$ is Weil complete if and only if the space $X$ is Dieudonn\'e complete. This result provides a positive answer to a question posed by the first listed…

Let $\Lambda X$ be the free loop space on a simply connected finite $CW$-complex $X$ and $\beta_{i}(\Lambda X;\Bbbk)$ be the cardinality of a minimal generating set of $H^{i}(\Lambda X;\Bbbk)$ for $\Bbbk$ to be a commutative ring with unit.…

This paper is the second in a series investigating cartesian closed varieties. In first of these, we showed that every non-degenerate finitary cartesian variety is a variety of sets equipped with an action by a Boolean algebra B and a…

Given weakly exact tracial von Neumann algebras $M_{1}, M_{2}$ with a common injective amalgam $B$, we prove that the amalgamated free product $M_{1}\overline{*}_{B}M_{2}$ is biexact relative to $\{M_{1},M_{2}\}$. In the case where $ M_1 $…

We investigate the sequential topology $\tau_s$ on a complete Boolean algebra $B$ determined by algebraically convergent sequences in $B$. We show the role of weak distributivity of $B$ in separation axioms for the sequential topology. The…

We prove a Theorem about the relationship between the Depth of the ultraproduct of Boolean algebras, divided by an ultrafilter, and the products of the depths of each component. This answers (partly) an open problem of Monk.

It is proved that fundamental groups of boolean representable simplicial complexes are free and the rank is determined by the number and nature of the connected components of their graph of flats for dimension $\geq 2$. In the case of…

In [Sh:89] we, answering a question of Monk, have explicated the notion of ``a Boolean algebra with no endomorphisms except the ones induced by ultrafilters on it'' (see section 2 here) and proved the existence of one with character density…

For any reduced free product $\mathrm{C}^*$-algebra $(A, \varphi) =(A_1, \varphi_1) \star (A_2, \varphi_2)$, we prove a boundary rigidity result for the embedding of $A$ into its associated $\mathrm{C}^*$-algebra $\Delta \mathbf{T}(A,…

We show that, in a highest weight category with duality, the endomorphism algebra of a tilting object is naturally a cellular algebra. Our proof generalizes a recent construction of Andersen, Stroppel, and Tubbenhauer. This result raises…

We prove in ZFC that for mu >= aleph_2 there is a sigma --ideal I on mu and a Boolean sigma --subalgebra B of the family of subsets of mu which includes I such that the natural homomorphism from B onto B/I cannot be lifted.

We consider two relatively natural topologizations of the set of all cellular automata on a fixed alphabet. The first turns out to be rather pathological, in that the countable space becomes neither first-countable nor sequential. Also,…

Consider some non-zero complex numbers $a_i, b_i, c_i, d_i$ with $1 \leq i \leq n$ and the associated classical Lotka-Volterra systems \[ \begin{cases} x' = a_i xy + b_i y \newline y' = c_i xy + d_i y \text{ .} \end{cases} \] We show that…

Complete Boolean algebras proved to be an important tool in topology and set theory. Two of the most prominent examples are B(kappa), the algebra of Borel sets modulo measure zero ideal in the generalized Cantor space {0,1}^kappa equipped…