제목 : Free resolutions for representations
연사 : Dong-il Lee (이동일) 박사
소속 : KIAS
날짜 : 12월 10일 수요일 (16:30~17:30)
장소 : ASARC 세미나실 (#1409)
초록 :The purpose of this talk is to introduce and generalize the notion of
Castelnuovo-Mumford regularity for representations of noncommutative algebras,
effectively establishing a measure of complexity for such objects. We study how to
compute free resolutions of modules over a noncommutative algebra.
The Groebner-Shirshov basis theory plays a crucial role in computing syzygies.
The uniqueness of minimal graded free resolutions can be readily established, from
which the notion of projective dimension and regularity for graded modules follows. Some interesting examples are included in which graded free resolutions and
regularities are computed for representations of various algebras.! In particular, using the Bernstein-Gelfand-Gelfand resolutions for integrable highest weight modules
over Kac-Moody algebras, we compute the projective dimensions and regularities
explicitly for the cases of finite and affine types.
This research is jointly worked with Professor Seok-Jin Kang, Professor Hyungju
Park and graduate student Euiyong Park.