Lie algebras and triple systems

This thesis is dedicated to the Tits-Kantor-Koecher (TKK) construction which establishes a bijective correspondence between unital Jordan algebras and shortly graded Lie algebras with Z-grading induced by an sl_2-triple. It is based on the observation that if g is a Lie algebra with a short Z-grading and f lies in g_1, then the formula ab=[[a,f],b] defines a structure of a Jordan algebra on g_{-1}. The TKK construction has been extended to Jordan triple systems and, more recently, to the so-called Kantor triple systems. These generalizations are studied in the thesis.

Applying partial virtualization on ELF binaries through dynamic loaders

The technology of partial virtualization is a revolutionary approach to the world of virtualization. It lies directly in-between full system virtual machines (like QEMU or XEN) and application-related virtual machines (like the JVM or the CLR). The ViewOS project is the flagship of such technique, developed by the Virtual Square laboratory, created to provide an abstract view of the underlying system resources on a per-process basis and work against the principle of the Global View Assumption. Virtual Square provides several different methods to achieve partial virtualization within the ViewOS system, both at user and kernel levels. Each of these approaches have their own advantages and shortcomings. This paper provides an analysis of the different virtualization methods and problems related to both the generic and partial virtualization worlds. This paper is the result of an in-depth study and research for a new technology to be employed to provide partial virtualization based on ELF dynamic binaries. It starts with a mild analysis of currently available virtualization alternatives and then goes on describing the ViewOS system, highlighting its current shortcomings. The vloader project is then proposed as a possible solution to some of these inconveniences with a working proof of concept and examples to outline the potential of such new virtualization technique. By injecting specific code and libraries in the middle of the binary loading mechanism provided by the ELF standard, the vloader project can promote a streamlined and simplified approach to trace system calls. With the advantages outlined in the following paper, this method presents better performance and portability compared to the currently available ViewOS implementations. Furthermore, some of itsdisadvantages are also discussed, along with their possible solutions.