Generators of simple Lie algebras in arbitrary characteristics

In this paper we study the minimal number of generators for simple Lie algebras in characteristic 0 or p > 3. We show that any such algebra can be generated by 2 elements. We also examine the 'one and a half generation' property, i.e. when every non-zero element can be completed to a generating pair. We show that classical simple algebras have this property, and that the only simple Cartan type algebras of type W which have this property are the Zassenhaus algebras.Comment: 26 pages, final version, to appear in Math. Z. Main improvements and corrections in Section 4.

PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces

This is the first of two articles in which we give a proof - for a broad class of four-manifolds - of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the four-manifold. This article is a revision of sections 1-3 of an earlier version of the article dg-ga/9712005, now split into two parts, while a revision of sections 4-7 of that earlier version appears in a recently updated dg-ga/9712005. In the present article, we construct virtual normal bundles for the Seiberg-Witten strata of the moduli space of PU(2) monopoles and compute their Chern classes.Comment: Journal fur die Reine und Angewandte Mathematik, to appear; 64 page

Jacobson generators, Fock representations and statistics of sl(n+1)

The properties of A-statistics, related to the class of simple Lie algebras sl(n+1) (Palev, T.D.: Preprint JINR E17-10550 (1977); hep-th/9705032), are further investigated. The description of each sl(n+1) is carried out via generators and their relations, first introduced by Jacobson. The related Fock spaces W_p (p=1,2,...) are finite-dimensional irreducible sl(n+1)-modules. The Pauli principle of the underlying statistics is formulated. In addition the paper contains the following new results: (a) The A-statistics are interpreted as exclusion statistics; (b) Within each W_p operators B(p)_1^\pm, ..., B(p)_n^\pm, proportional to the Jacobson generators, are introduced. It is proved that in an appropriate topology the limit of B(p)_i^\pm for p going to infinity is equal to B_i^\pm, where B_i^\pm are Bose creation and annihilation operators; (c) It is shown that the local statistics of the degenerated hard-core Bose models and of the related Heisenberg spin models is p=1 A-statistics.Comment: LaTeX-file, 33 page

Compactifications and algebraic completions of Limit groups

In this paper we consider the existence of dense embeddings of Limit groups in locally compact groups generalizing earlier work of Breuillard, Gelander, Souto and Storm [GBSS] where surface groups were considered. Our main results are proved in the context of compact groups and algebraic groups over local fields. In addition we prove a generalization of the classical Baumslag lemma which is a useful tool for generating eventually faithful sequences of homomorphisms. The last section is dedicated to correct a mistake from [BGSS] and to get rid of the even genus assumption.Comment: v2: Substantial changes to sections 7 and 8.2. Typos corrected. References added. v3: Acknowledgement correcte

Oxidation-resistant multilayer coatings using an anodic alumina layer as a diffusion barrier on γ-TiAl substrates

Diffusion barrier layers of anodic alumina, introduced between an oxidation-resistant Al-Nb-Cr alloy and γ-TiAl substrate, have been evaluated using scanning electron microscopy and electron probe microanalysis. Diffusion of titanium to the Al-Nb-Cr coating is obvious when the Al-Nb-Cr alloy coated directly on the TiAl substrate is oxidized at 900°C for 168 h. The anodic alumina layer has been introduced by sputter-depositing aluminum and subsequent anodizing of the aluminum layer at a constant current density in 0.01 mol dm-3 ammonium pentaborate electrolyte at 298 K. Then, the Al-Nb-Cr alloy is further sputter-deposited on the anodized specimens. It is clearly demonstrated that the thin anodic alumina layer, less than 500 nm thick, suppresses effectively the inter-diffusion between the oxidation-resistant alloy coating and the TiAl substrate, particularly when a thin aluminum layer is remained beneath the anodic alumina. Although microcracks are generated and the substrate is oxidized through the cracked regions for the coatings that contain the metallic aluminum layer, the oxidation of the substrate through the cracks is prevented by pre-oxidation treatment at 800°C