We will consider various types of identities of matrix algebras. Trace identities are a generalisation of polynomial identities, and every trace identity is a consequence of the Cayley-Hamilton identity by the second fundamental theorem of matrix invariants. We will show that this is no longer the case for quasi-identities, while it holds for functional identities. We will also present an application of matrix invariants to free analysis.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5312