Sofic mean length
Amenability, coarse embeddability and fixed point properties December 06, 2016  December 09, 2016
Location: SLMath: Atrium
sofic groups
module
module theory
groups of units
Amenability
aTmenability
fixed point properties
hyperbolic group
Banach space
group cohomology
expander graph
index theory
noncommutative geometry
16U80  Generalizations of commutativity (associative rings and algebras)
00A35  Methodology of mathematics {For mathematics education, see 97XX}
00B25  Proceedings of conferences of miscellaneous specific interest
00B55  Collections of translated articles of miscellaneous specific interest
0111  Research data for problems pertaining to history and biography
20E15  Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
14644
For a unital ring R, a length function on left Rmodules 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 Rmodules equipped with a Gaction. I will discuss the question of how to define a length function for RGmodules, given a length function for Rmodules. An application will be given to the question of direct finiteness of RG, i.e. whether every onesided invertible element of RG is twosided invertible. This is based on joint work with Bingbing Liang
Li Notes

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