Jakub Bulin (CU Boulder) The Bounded Width Theorem, Part 1
Nov. 10, 2015 2pm (MATH 350)
Lie Theory
Ed Green (Virginia Tech)
X
Brauer tress were introduced in 1970s in the study of finite group rings over fields of characteristic p. In the 1980s they were generalized to Brauer graphs. Brauer graph algebras are biserial and tame (terms I will define in my talk). Together with Sybille Schroll of Univ. of Leicester, England, we have been able to generalize such algebras to Brauer configuration algebras, which are mostly wild. I will describe these symmetric algebras and their relationship to multiserial algebras and some properties of their modules.
We will continue last week's discussion, beginning by developing the language of vector fields on subcartesian spaces. Using this language, we will outline the proof that the orbit-type stratification on the orbit space coming from a Lie group action that is proper and Poisson is in fact a Poisson stratification; that is, the strata are Poisson submanifolds.
We then specialise to the case of a Hamiltonian group action, and define symplectic reduction. Here, the symplectic quotient is a quotient space of a level set of the momentum map. We will show that in this case, the orbit-type stratification on the symplectic quotient is a symplectic stratification; that is, the strata are symplectic submanifolds.