Lifting of Quantum Linear Spaces and Pointed Hopf Algebras of order p^3

We propose the following principle to study pointed Hopf algebras, or more generally, Hopf algebras whose coradical is a Hopf subalgebra. Given such a Hopf algebra A, consider its coradical filtration and the associated graded coalgebra grad(A). Then grad(A) is a graded Hopf algebra, since the coradical A_0 of A is a Hopf subalgebra. In addition, there is a projection \pi: grad(A) \to A_0; let R be the algebra of coinvariants of \pi. Then, by a result of Radford and Majid, R is a braided Hopf algebra and grad(A) is the bosonization (or biproduct) of R and A_0: grad(A) is isomorphic to (R # A_0). The principle we propose to study A is first to study R, then to transfer the information to grad(A) via bosonization, and finally to lift to A. In this article, we apply this principle to the situation when R is the simplest braided Hopf algebra: a quantum linear space. As consequences of our technique, we obtain the classification of pointed Hopf algebras of order p^3 (p an odd prime) over an algebraically closed field of characteristic zero; with the same hypothesis, the characterization of the pointed Hopf algebras whose coradical is abelian and has index p or p^2; and an infinite family of pointed, non-isomorphic, Hopf algebras of the same dimension. This last result gives a negative answer to a conjecture of I. Kaplansky.Comment: AmsTeX, 28 pages. To be published in J. of Algebr

Evidence for charged critical behavior in the pyrochlore superconductor RbOs2O6

We analyze magnetic penetration depth data of the recently discovered superconducting pyrochlore oxide RbOs2O6. Our results strongly suggest that in RbOs2O6 charged critical fuctuations dominate the temperature dependence of the magnetic penetration depth near Tc. This is in contrast to the mean-field behavior observed in conventional superconductors and the uncharged critical behavior found in nearly optimally doped cuprate superconductors. However, this finding agrees with the theoretical predictions for charged criticality and the charged criticality observed in underdoped YBa2Cu3O6.59.Comment: 5 pages, 4 figure

The design and construction of the CAD-1 airship

The background history, design philosophy and Computer application as related to the design of the envelope shape, stress calculations and flight trajectories of the CAD-1 airship, now under construction by Canadian Airship Development Corporation are reported. A three-phase proposal for future development of larger cargo carrying airships is included

Generalized Robba rings

We prove that any projective coadmissible module over the locally analytic distribution algebra of a compact $p$-adic Lie group is finitely generated. In particular, the category of coadmissible modules does not have enough projectives. In the Appendix a "generalized Robba ring" for uniform pro-$p$ groups is constructed which naturally contains the locally analytic distribution algebra as a subring. The construction uses the theory of generalized microlocalization of quasi-abelian normed algebras that is also developed there. We equip this generalized Robba ring with a self-dual locally convex topology extending the topology on the distribution algebra. This is used to show some results on coadmissible modules.Comment: with an appendix by Peter Schneider; revised; new titl