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Sofic mean length

Amenability, coarse embeddability and fixed point properties December 06, 2016 - December 09, 2016

December 07, 2016 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Hanfeng Li (University at Buffalo (SUNY))
Location: MSRI: Atrium
Tags/Keywords
  • sofic groups

  • module

  • module theory

  • groups of units

  • Amenability

  • a-T-menability

  • fixed point properties

  • hyperbolic group

  • Banach space

  • group cohomology

  • expander graph

  • index theory

  • non-commutative geometry

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

14644

Abstract

For a unital ring R, a length function on left R-modules assigns a (possibly infinite) nonnegative number to each module being additive for short exact sequences of modules. For any unital ring R and any group G, one can form the group ring RG of G with coefficients in R. The modules of RG are exactly R-modules equipped with a G-action. I will discuss the question of how to define a length function for RG-modules, given a length function for R-modules. An application will be given to the question of direct finiteness of RG, i.e. whether every one-sided invertible element of RG is two-sided invertible. This is based on joint work with Bingbing Liang

Supplements
27472?type=thumb Li Notes 3.24 MB application/pdf Download
Video/Audio Files

14644

H.264 Video 14644.mp4 367 MB video/mp4 rtsp://videos.msri.org/data/000/027/237/original/14644.mp4 Download
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