主讲人：Prof. Sui Por LAM（林兆波)（英国剑桥大学）

时  间：10月29日（周二）16:00-17:00

地  点：必赢76net线路官网北二区教学楼 517 教室

摘  要: The class of Lie groups are known to have their algebraic topology computable. The first example is Hopf's theorem on the rational cohomology of simply connected compact Lie groups; they turn out to be exterior algebras over Q in generators of odd degrees. Of course this does not hold over the integers because of torsions. However through the eyes of K-theory, they behave even better. Hodgkin showed that the K-theory of any simply connected compact Lie group is an exterior algebra with generators in K^1. This holds without localising. In the 90s, Brylinsky and Zhang showed that if G is a simply connected compact Lie group acting on itself by the adjoint action (also known as conjugation action), then the equivariant K-thery of G is an exterior algebra over R(G) (the representation ring of G) in generators in K^1, and the generators correspond to the basic representations of G. Incidentally if G acts on itself trivially, the equivariant K-theory of G has the same structure and this follows trivially from Hodgkin's result. We will show that if G is as above, H is any compact Lie group, f: H-->G is any group homomorphism, then the equivariant K-theory of G (considered as an H-space where H acts on G via f followed by conjugation) is an exterior algebra over R(H) in generators in K^1 corresponding to the basic representations of G. In particular, if H=G and f is any self homomorphism, then the equivariant K-theory of G has the same structure, generalising the result of Hodgkin and that of Brylinsky-Zhang. Also this is in sharp contrast with the Real case where the algebra structure is dependent on the homomorphism.