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.

Presentations: from Kac-Moody groups to profinite and back

We go back and forth between, on the one hand, presentations of arithmetic and Kac-Moody groups and, on the other hand, presentations of profinite groups, deducing along the way new results on both

Location, location, location: utilizing pipelines and services to more effectively georeference the world's biodiversity data

Abstract Background Increasing the quantity and quality of data is a key goal of biodiversity informatics, leading to increased fitness for use in scientific research and beyond. This goal is impeded by a legacy of geographic locality descriptions associated with biodiversity records that are often heterogeneous and not in a map-ready format. The biodiversity informatics community has developed best practices and tools that provide the means to do retrospective georeferencing (e.g., the BioGeomancer toolkit), a process that converts heterogeneous descriptions into geographic coordinates and a measurement of spatial uncertainty. Even with these methods and tools, data publishers are faced with the immensely time-consuming task of vetting georeferenced localities. Furthermore, it is likely that overlap in georeferencing effort is occurring across data publishers. Solutions are needed that help publishers more effectively georeference their records, verify their quality, and eliminate the duplication of effort across publishers. Results We have developed a tool called BioGeoBIF, which incorporates the high throughput and standardized georeferencing methods of BioGeomancer into a beginning-to-end workflow. Custodians who publish their data to the Global Biodiversity Information Facility (GBIF) can use this system to improve the quantity and quality of their georeferences. BioGeoBIF harvests records directly from the publishers' access points, georeferences the records using the BioGeomancer web-service, and makes results available to data managers for inclusion at the source. Using a web-based, password-protected, group management system for each data publisher, we leave data ownership, management, and vetting responsibilities with the managers and collaborators of each data set. We also minimize the georeferencing task, by combining and storing unique textual localities from all registered data access points, and dynamically linking that information to the password protected record information for each publisher. Conclusion We have developed one of the first examples of services that can help create higher quality data for publishers mediated through the Global Biodiversity Information Facility and its data portal. This service is one step towards solving many problems of data quality in the growing field of biodiversity informatics. We envision future improvements to our service that include faster results returns and inclusion of more georeferencing engines