Semisimple Lie algebras and their Casimir operators have played a fundamental role in the development and description of a raft of physical problems. Non-semisimple Lie algebras, on the other hand, are only understood in very few cases. In particular the classification of their Casimir invariants remains an open problem. For the ubiquitous (centrally extended) Schrodinger algebras, for example, the Casimir invariants have only been constructed very recently. This was achieved using the so-called virtual copy approach, which is believed to be generalisable to a vast class of algebras. This project intends to develop further these ideas and results. This will give crucial insight into the very complex representation theory of non-semisimple Lie algebras.

Project members

Supervisor: Ian Marquette

Dr Ian Marquette

ARC Future Fellowship