Sofic mean length
Amenability, coarse embeddability and fixed point properties December 06, 2016 - December 09, 2016
Location: MSRI: Atrium
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
22D25 - $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]
43-XX - Abstract harmonic analysis {For other analysis on topological and Lie groups, see 22Exx}
46-XX - Functional analysis {For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx}
57-XX - Manifolds and cell complexes {For complex manifolds, see 32Qxx}
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
14644
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
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14644
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