Islam's Foundational Equality

In Feminist Edges of the Qur’an, Aysha Hidayatullah argues that certain Qur’anic verses are incorrigibly male-privileging and are themselves privileged. Hence, egalitarian readings of the Qur’an are unsupported and unsupportable. If, as egalitarians propose, such verses are unjust, then either the Qur’an is not God’s word or God is unjust. By contrast, I argue that no evidence suggests any such verses are incorrigibly male- privileging. Further I indicate egalitarian rereadings for relevant contenders and note that, in any case, no Qur’anic evidence warrants the primacy of such verses. Finally, since controverting egalitarian readings of such verses are available, the logical form of Hidayatullah’s argument merely shows that if they are read to exhibit injustice, those readings cannot be God’s word. Since believers hold that the Qur’an is God’s word, there is no option but to reread them

Fundamental groupoids of k-graphs

k-graphs are higher-rank analogues of directed graphs which were first developed to provide combinatorial models for operator algebras of Cuntz-Krieger type. Here we develop a theory of the fundamental groupoid of a k-graph, and relate it to the fundamental groupoid of an associated graph called the 1-skeleton. We also explore the failure, in general, of k-graphs to faithfully embed into their fundamental groupoids.Comment: 12 page

Skew-products of higher-rank graphs and crossed products by semigroups

We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the $C^*$-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the $C^*$-algebra of a quotient graph. Our main tool is Laca's dilation theory for endomorphic actions of Ore semigroups on $C^*$-algebras, which embeds such an action in an automorphic action of the enveloping group on a larger $C^*$-algebra.Comment: 14 pages. Accepted by Semigroup Foru

Periodic 2-graphs arising from subshifts

Higher-rank graphs were introduced by Kumjian and Pask to provide models for higher-rank Cuntz-Krieger algebras. In a previous paper, we constructed 2-graphs whose path spaces are rank-two subshifts of finite type, and showed that this construction yields aperiodic 2-graphs whose $C^*$-algebras are simple and are not ordinary graph algebras. Here we show that the construction also gives a family of periodic 2-graphs which we call \emph{domino graphs}. We investigate the combinatorial structure of domino graphs, finding interesting points of contact with the existing combinatorial literature, and prove a structure theorem for the $C^*$-algebras of domino graphs.Comment: 17 page

The Long Reformation of the Dead in Scotland

This thesis argues that, although attempts were initially made at the Reformation of 1560 to reform Scottish burial practices, and thereafter further attempts were made fairly consistently throughout the following decades and centuries, it was actually not until the Disruption of 1843 and subsequent events that there was any true measure of success in the reform of Scottish burial practices. Prior to the Reformation Scotland was a Catholic nation, although in terms of burial practices it was somewhat different to other Catholic countries. This individuality of burial practice was to continue throughout the three centuries covered by this thesis. Following the Reformation attempts were made by the various Kirk authorities throughout Scotland to reform burial practice along Protestant lines. These attempts were largely uniform throughout Scotland, although certain regional variations existed, for instance attempts made to ban practices such as the coronach in the Highlands and Islands. Some of these attempts were successful, others were less so. Additionally, reforms aimed at the lower social orders were more successful, on the whole, than those aimed at the upper classes, as the upper classes could afford to pay nominal fines after a breach of the rules concerning burial. However, over the period the goals of the early reformers to ensure that in death all were seen to be equal, regardless of class or social status, and the removal of practices deemed to be superstitious or intercessory, were more or less ignored. By the time of the Disruption burial practice in Scotland was barely related to the ideals of Knox and the other early Scottish reformers. However, with the expulsion of the Free Church of Scotland from the Kirk owned burial grounds, new locations had to be sought. These were ultimately found in the newly opened public cemeteries. These were locations set aside for burial alone, and were not consecrated, two of the core ideals of the early Scottish reformers. Additionally, there were no graveside sermons and no attempts at intercession on behalf of the dead. Finally, after three centuries, at least one group of Scottish Presbyterians had almost fully embraced the reformation of the dead

Rank-two graphs whose C^*-algebras are direct limits of circle algebras

We describe a class of rank-2 graphs whose C^*-algebras are AT algebras. For a subclass which we call rank-2 Bratteli diagrams, we compute the K-theory of the C*-algebra. We identify rank-2 Bratteli diagrams whose C*-algebras are simple and have real-rank zero, and characterise the K-invariants achieved by such algebras. We give examples of rank-2 Bratteli diagrams whose C*-algebras contain as full corners the irrational rotation algebras and the Bunce-Deddens algebras.Comment: 41 pages, uses pictex for figure

A family of 2-graphs arising from two-dimensional subshifts

Higher-rank graphs (or $k$-graphs) were introduced by Kumjian and Pask to provide combinatorial models for the higher-rank Cuntz-Krieger $C^*$-algebras of Robertson and Steger. Here we consider a family of finite 2-graphs whose path spaces are dynamical systems of algebraic origin, as studied by Schmidt and others. We analyse the $C^*$-algebras of these 2-graphs, find criteria under which they are simple and purely infinite, and compute their $K$-theory. We find examples whose $C^*$-algebras satisfy the hypotheses of the classification theorem of Kirchberg and Phillips, but are not isomorphic to the $C^*$-algebras of ordinary directed graphs.Comment: 28 pages, 3 figures, 1 tabl

Strong Shift Equivalence of C∗C^*-correspondences

We define a notion of strong shift equivalence for $C^*$-correspondences and show that strong shift equivalent $C^*$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift equivalent square matrices with non-negative integer entries give stably isomorphic Cuntz-Krieger algebras.Comment: 26 pages. Final version to appear in Israel Journal of Mathematic