Deformation of algebras over the Landweber-Novikov algebra

An algebraic deformation theory of algebras over the Landweber-Novikov algebra is obtained.Comment: Improved Proposition 2.4. To appear in Journal of Algebr

A dichotomy for groupoid C*-algebras

We study the finite versus infinite nature of C*-algebras arising from etale groupoids. For an ample groupoid G, we relate infiniteness of the reduced C*-algebra of G to notions of paradoxicality of a K-theoretic flavor. We construct a pre-ordered abelian monoid S(G) which generalizes the type semigroup introduced by R{\o}rdam and Sierakowski for totally disconnected discrete transformation groups. This monoid reflects the finite/infinite nature of the reduced groupoid C*-algebra of G. If G is ample, minimal, and topologically principal, and S(G) is almost unperforated we obtain a dichotomy between stable finiteness and pure infiniteness for the reduced C*-algebra of G.Comment: 40 pages. Version 2: Section 9.2 updated to reflect intersection with earlier results of Suzuki; thanks to Suzuki for alerting us. Proofs of Proposition 5.2 and Lemma 9.7 simplified using the refinement property (correcting an oversight in the proof of Proposition 5.2

Irreducible Highest Weight Representations Of The Simple n-Lie Algebra

A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of all irreducible, highest weight modules, including the infinite-dimensional ones. As a corollary we find all primitive ideals of the universal enveloping algebra of this simple n-Lie algebra.Comment: 24 pages, 24 figures, mistake in proposition 2.1 correcte