The Prime Spectrum and Representation Theory of the 2×22\times 2 Reflection Equation Algebra

The theory of generalized Weyl algebras is used to study the $2\times 2$ reflection equation algebra $\mathcal{A}=\mathcal{A}_q(\operatorname{M}_2)$ in the case that $q$ is not a root of unity, where the $R$-matrix used to define $\mathcal{A}$ is the standard one of type $A$. Simple finite dimensional $\mathcal{A}$-modules are classified, finite dimensional weight modules are shown to be semisimple, $\operatorname{Aut}(\mathcal{A})$ is computed, and the prime spectrum of $\mathcal{A}$ is computed along with its Zariski topology. Finally, it is shown that $\mathcal{A}$ satisfies the Dixmier-Moeglin equivalence

Weak amenability and 2-weak amenability of Beurling algebras

Let L^1_\om(G) be a Beurling algebra on a locally compact abelian group $G$. We look for general conditions on the weight which allows the vanishing of continuous derivations of L^1_\om(G). This leads us to introducing vector-valued Beurling algebras and considering the translation of operators on them. This is then used to connect the augmentation ideal to the behavior of derivation space. We apply these results to give examples of various classes of Beurling algebras which are weakly amenable, 2-weakly amenable or fail to be even 2-weakly amenable.Comment: 25 page

Spanning trees and even integer eigenvalues of graphs

For a graph $G$, let $L(G)$ and $Q(G)$ be the Laplacian and signless Laplacian matrices of $G$, respectively, and $\tau(G)$ be the number of spanning trees of $G$. We prove that if $G$ has an odd number of vertices and $\tau(G)$ is not divisible by $4$, then (i) $L(G)$ has no even integer eigenvalue, (ii) $Q(G)$ has no integer eigenvalue $\lambda\equiv2\pmod4$, and (iii) $Q(G)$ has at most one eigenvalue $\lambda\equiv0\pmod4$ and such an eigenvalue is simple. As a consequence, we extend previous results by Gutman and Sciriha and by Bapat on the nullity of adjacency matrices of the line graphs. We also show that if $\tau(G)=2^ts$ with $s$ odd, then the multiplicity of any even integer eigenvalue of $Q(G)$ is at most $t+1$. Among other things, we prove that if $L(G)$ or $Q(G)$ has an even integer eigenvalue of multiplicity at least $2$, then $\tau(G)$ is divisible by $4$. As a very special case of this result, a conjecture by Zhou et al. [On the nullity of connected graphs with least eigenvalue at least $-2$, Appl. Anal. Discrete Math. 7 (2013), 250--261] on the nullity of adjacency matrices of the line graphs of unicyclic graphs follows.Comment: Final version. To appear in Discrete Mat

Placing the Normative Logics of Accountability in Thick Perspective

This paper provides a critical reflection on the heavily normative nature of current accountability debates. In particular, three streams of normative discourse on nonprofit accountability are identified: improving board governance; improving performance-based reporting; and, demonstrating progress towards mission. A focus on these normative logics, while important, can mask the realities of social structure and the relations of power that underlie them. The paper thus proposes a more empirical approach to framing accountability problems thick description and interpretation that might enable us better to understand how social regimes of accountability actually operate and in which the instruments of accountability are at least as likely to reproduce relationships of inequality as they are to overturn them.This publication is Hauser Center Working Paper No. 33.2. Hauser Working Paper Series Nos. 33.1-33.9 were prepared as background papers for the Nonprofit Governance and Accountability Symposium October 3-4, 2006

Divine Love and the Argument from Divine Hiddenness

This paper criticizes one of the premises of Schellenberg’s atheistic argument from divine hiddenness. This premise, which can be considered as the foundation of his proposed argument, is based on a specific interpretation of divine love as eros. In this paper I first categorize several concepts of divine love under two main categories, eros and agape; I then answer some main objections to the ascription of eros to God; and in the last part I show that neither on a reading of divine love as agape nor as eros can Schellenberg’s argument be construed as sound. My aim is to show that even if -- contra Nygren for example -- we accept that divine love can be interpreted as eros, Schellenberg’s argument still doesn’t work