The quantum revolution in physics has inspired new directions in mathematical research, by introducing new kinds of non-commutative structures. EU-funded mathematicians have recently established extensions of C*-algebras.
In quantum physics, scientists often start by taking classical observables and writing down formulas that imply that these observables do not commute. In doing so, they define an algebra, usually called ‘algebra of observables’. C*-algebras are a way of making the results of this process more precise.
Further details: Non-commutative structures in quantum physics