quantum_group

# Quantum group

Symmetry in non-commutative geometry

A quantum group is (sort of) generalization of a group. Roughly, one replaces a group $G$ by a matrix-analog of the space of functions $\mathrm{Fun}(G,\mathbb{C})$. They appear in the study of symmetries in non-commutative geometry, but also in representation theory of Lie algebras, knot theory, and many other areas.

## Material

An article in the series Snapshots of modern mathematics from Oberwolfach giving a very elementary introduction:

• Lie algebras
• Hopf algebras