제목 : Projectivity of certain non-commutative $L_p$ spaces as modules over Fourier algebra
연사 : Lee, Hun Hee(이훈희) 박사
소속 : University of Waterloo
날짜 : 11월 6일 목요일 (16:00~17:00)
장소 : 산업경영동 세미나실(#2222)
초록: Dales and Polyakov (2004) investigated projectivity (amongother homological properties) of various left $L^1(G)$-modules for any locally compact group $G$.The class of modules include $L^p(G)$ for $1< p<\infty$. They proved that $L^p(G)$ for $1projective if and only if $G$ is compact.
In this talk we focus on the dual situation, namely $A(G)$-modules$L^p(VN(G))$ for $1. We will show that $L^p(VN(G))$ for $1an operator projective left $A(G)$-module when $G$ is discrete and amenable.Conversely, we can show that $L^p(VN(G))$ for $2\lep <\infty$ is not operator projective when $G$ is a non-discrete group.Unlike in the case of $L^1(G)$-modules amenability plays an important role here. Indeed, $L^p(VN(G))$ for $1 projective left operator $A(G)$-modulewhen $G = \mathbb{F}_2$, the free groupwith two generators.