On homological properties for some modules of uniformly continuous functions

ON HOMOLOGICAL PROPERTIES FOR SOME MODULES OF UNIFORMLY CONTINUOUS FUNCTIONS OVER
CONVOLUTION ALGEBRAS

RASOUL NASR-ISFAHANI

 SIMA SOLTANI RENANI

Abstract: For a locally compact group G, let LUC.G/ denote the space of all left uniformly continuous functions
on G. Here, we investigate projectivity, injectivity and flatness of LUC.G/ and its dual space LUC.G/
as Banach left modules over the group algebra as well as the measure algebra of G.
2010 Mathematics subject classification: primary 43A07; secondary 43A15, 43A20, 46H05, 46H25.
Keywords and phrases: amenability, flatness, injectivity, projectivity, Banach module, locally compact
group.