An automaton-theoretic approach to the representation theory of quantum algebras

We develop a new approach to the representation theory of quantum algebras supporting a torus action via methods from the theory of finite-state automata and algebraic combinatorics. We show that for a fixed number $m$, the torus-invariant primitive ideals in $m\times n$ quantum matrices can be seen as a regular language in a natural way. Using this description and a semigroup approach to the set of Cauchon diagrams, a combinatorial object that paramaterizes the primes that are torus-invariant, we show that for $m$ fixed, the number of torus-invariant primitive ideals in $m\times n$ quantum matrices satisfies a linear recurrence in $n$ over the rational numbers. In the $3\times n$ case we give a concrete description of the torus-invariant primitive ideals and use this description to give an explicit formula for the number P(3,n).Comment: 31 page

1. REPORT ON A COLLECTION OF ANIMALS FROM MADAGASCAR, TRANSMITTED TO THE SOCIETY

Volume: 1865Start Page: 467End Page: 47

The Nile on the move

The Nile, as a meandering river, has moved relative to habitation sites since antiquity, as attested in historic documents. Geologists Katy Lutley and Juditl Bunbury combined maps and satellite images with a walk-about in the Caio area to propose a map for its past movements.Their results suggest that enviionmental change has been topical since the Old Kingdo

The stable rank of diagonal ASH algebras and crossed products by minimal homeomorphisms

We introduce a subclass of recursive subhomogeneous algebras, in which each of the pullback maps is diagonal in a suitable sense. We define the notion of a diagonal map between two such algebras and show that every simple inductive limit of these algebras with diagonal bonding maps has stable rank one. As an application, we prove that, for any infinite compact metric space T and minimal homeomorphism h : T → T, the associated dynamical crossed product C*(Z, T, h) has stable rank one. This affirms a conjecture of Archey, Niu, and Phillips. We also show that the Toms–Winter Conjecture holds for such crossed products

Giza Geomorphological Report in Giza Plateau Mapping Project Seasons 2006-2007 Preliminary Report

We have constructed a preliminary map of the locations of the Nile since the Old Kingdom from observations of historic maps, satellite images, and recent topographic survey. In addition to this work, we have made a walking tour of the Giza urban environment and find that patters in the landscape are remarkably persistent. Our results suggest that the pyramids were built close to a branch of the Nile but that this branch moved rapidly eastwards from the pyramid site with time

Allen on Birds Collected in Bolivia

Volume: 7Start Page: 381End Page: 38