In the context of Operator Algebra Theory, `Quantum' means a noncommutative generalization of classical objects in terms of Gelfand duality, which states that the category of compact spaces is dual to the category of COMMUTATIVE unital C*-algebras. Regarding general NON-COMMUTATIVE C*-algebras as function algebras over `quantum' spaces, we reach the concept of non-commutative geometry. As a powerful application of this perspective, we will review the well-established theory of quantum groups. After that, we will see how to quantize the notion of graphs consisting of vertices and edges from a function-algebraic viewpoint. Simply speaking, vertices are replaced with matrix algebras and edges with suitable linear operators between them. Quantum Graph Theory has developed over the past 14 years and has deepened the theory of quantum symmetry.

강연시간 : 16:40-17:10