Glider Representations
Student No.:50
Time:Friday 15:00-16:00, 2016-9-9
Instructor:Fred Van Oystaeyen  [University of Antwerp, Belgium]
Place:Conference Room 4, Floor 2, Jin Chun Yuan West Building
Starting Date:2016-9-9
Ending Date:2016-9-9




Glider representations depend on a filtration of a ring R with S as the part of degree zero. A glider is an S-module M contained in an R-module W ,with a descending chain of S-submodules M(i) for i in N, such that F(j)R.M(i) is in M(i-j) for j smaller than i .There are typically two kinds of filtrations in the application, one is where F(i)R is some subring R(i) of R, e.g., a chain of group rings corresponding to a chain of groups G(i) in a group G; a chain of enveloping algebras corresponding to a chain of Lie algebras in some Lie algebra over some field,....other examples of chains of coordinate rings of varieties, chains of iterated Ore extensions, chains of Quantum groups, also, provide interesting applications. The second type of filtration is of a geometric type, a so-called standard filtration stemming from a free algebra or a polynomial ring by passing to quotients. The glider representations yield a theory where the representations of chains of groups, algebras, Lie algebras,....,are linked together, so the representation contains information about the stepwise construction of the final object. We will provide some theory about the two types of filtrations. First concerning a Clifford theory for the glider representations of a chain of finite groups, secondly a scheme theory for gliders defined over some (noncommutative or commutative) geometric space defined over the filtered ring for so-called standard filtrations. The subject is in full development, interesting applications have now also been observed in Lie algebra root systems and singularities in varieties . There are very many new interesting research possibilities, for example what about chains of finite dimensional algebras and their quivers?. The material in the talk is stemming from joint work of me and F. Caenepeel.


Contact person: Bangming Deng