16th December – Alex: Quantum algebras and polynomial identity (PI) degrees

Quantum algebras arose in the 1980’s as deformations of the algebra of functions over certain groups and were motivated by problems in mathematical physics. Under certain conditions, the resulting quantum algebra is a so-called PI algebra and thus has a PI degree. I shall introduce quantum algebras and their motivation from the classical case, define the PI degree and say why it can be useful, and show how combinatorial diagrams can help when calculating the PI degree of some algebras.