A closed subgroup $H$ of a locally compact group $G$ is confined if the closure conjugacy class in Chabauty space does not contain trivial subgroup. We establish dynamical criterion on action totally disconnected $X$ ensuring that no relatively amenable can be confined. This property equivalent to fact its Furstenberg boundary free. Our applies Neretin groups. deduce each has two inequivalent i...

We develop a new symmetrized version of the Projector Quantum Monte Carlo (SPQMC) method which preserves the symmetries of the system by simultaneously sampling all symmetry related Ising configurations at each MC step and use it to study the effect of electron correlations on a single C60 molecule and its structural motifs, within the Hubbard model. Thi SPQMC method allows more accurate estima...

1. A complex Banach algebra A is a compact (weakly compact) algebra if its left and right regular representations consist of compact (weakly compact) operators. Let E be any subset of A and denote by Ei and Er the left and right annihilators of E. A is an annihilator algebra if A¡= (0) —Ar, Ir^{fS) for each proper closed left ideal / and Ji t¿ (0) for each proper closed right ideal /. In [6, Th...

A topological space X is said to be generated by an ideal I if for all A ⊆ X and all x ∈ A there is E ⊆ A in I such that x ∈ E, and is said to be weakly generated by I if whenever a subset A of X contains E for every E ⊆ A with E ∈ I, then A itself is closed. An important class of examples are the so called weakly discretely generated spaces (which include sequential, scattered and compact Haus...

Alexander duality has, in the past, made its way into commutative algebra through Stanley-Reisner rings of simplicial complexes. This has the disadvantage that one is limited to squarefree monomial ideals. The notion of Alexander duality is generalized here to arbitrary monomial ideals. It is shown how this duality is naturally expressed by Bass numbers, in their relations to the Betti numbers ...

In this paper we study irreducible representations of regular limit subalgebras of AF-algebras. The main result is twofold: every closed prime ideal of a limit of direct sums of nest algebras (NSAF) is primitive, and every prime regular limit algebra is primitive. A key step is that the quotient of a NSAF algebra by any closed ideal has an AF C*-envelope, and this algebra is exhibited as a quot...

Let ? be an irreducible unitary representation of a finitely generated non-abelian free group ?; suppose is weakly contained in the regular representation. In 2001 first and third authors conjectured that such must either odd or monotonous duplicitous. 2004 they introduced class multiplicative representations: this large representations obtained by looking at action ? on its Cayley graph. secon...

Let [Formula: see text] be a weighted oriented graph and its edge ideal. We provide one method to find all the minimal generators of text], where is maximal strong vertex cover intersections irreducible ideals associated covers contained in text]. If an induced digraph under certain condition on we show that for some implies necessary sufficient equality ordinary symbolic powers ideal union two...

We give a counterexample to a conjecture of S.E. Morris by showing that there is a compact plane set X such that R(X) has no non-zero, bounded point derivations but such that R(X) is not weakly amenable. We also give an example of a separable uniform algebra A such that every maximal ideal of A has a bounded approximate identity but such that A is not weakly amenable.