Quantum groups refer to certain noncommutative algebras, with additional structures called comultiplication, antipode and braiding. Because of these structures, representation theory of quantum groups is highly interesting in itself and has deep connections with other branches such as topology, geometry, mathematical physics and combinatorics.
In this talk, we review a construction of the most simple quantum group. We first define a quantum plane as a noncommutative deformation of the coordinate ring of the affine plane. Then the symmetry 'group' of the quantum plane should be the quantum GL(2). Here the main ingredient is an R-matrix, which naturally provides to the quantum group a braiding, the most important structure.
일시: 9월 6일 (화) 16:40-17:10