On Griess Algebras

In this paper we prove that for any commutative (but in general non-associative) algebra $A$ with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra $V = V_0 \oplus V_2 \oplus V_3\oplus ...$, such that $\dim V_0 = 1$ and $V_2$ contains $A$. We can choose $V$ so that if $A$ has a unit $e$, then $2e$ is the Virasoro element of $V$, and if $G$ is a finite group of automorphisms of $A$, then $G$ acts on $V$ as well. In addition, the algebra $V$ can be chosen with a non-degenerate invariant bilinear form, in which case it is simple.Comment: This is a contribution to the Special Issue on Kac-Moody Algebras and Applications, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Hybridity, Mestizaje, and Montubios in Ecuador

The 'Montubio' ethnic identity has recently gained notoriety in Ecuador. This paper analyses how this identity emerges from and falls within Ecuador's construction of 'mestizaje' or mixture as a tool for national integration. Given the exclusionary and limited nature of mestizaje in Ecuador, it is argued that as far as Montubios are uncritically constructed in relation to such mestizaje, they cannot serve as a progressive hybrid identity able to overcome essentialisms and existent ethnic structures. This paper starts by briefly reviewing how mestizaje has been constructed in Ecuador and then examines how the Montubio identity emerges from this mestizaje. It then explores different ways in which mestizaje may be conceptualized, and examines how these different models disguise or address power dynamics within heterogeneous populations. It concludes by briefly noting how 'translocational positionality' might provide a way to conceptualize the most progressive promises of mestizaje that Montubios might access.

Luzin and anti-Luzin almost disjoint families

Under MA_{omega_1} every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated

Complete integral closure and strongly divisorial prime ideals

It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without {\em prime} strongly divisorial ideals is not necessarily completely integrally closed, although this property holds under some additional assumptions.Comment: 18 page