In this paper we initiate the study of real group algebras and investigate some of its aspects. Let 1 L ) (G be a group algebra of a locally compact group G G G → : ,τ be a group homeomorphism such that 1 2 = = τοτ τ , the identity map, and } : ) ( { ) , ( f f G L f G L p p = ∈ = οτ τ ) 1 ( ≥ p . In this paper, among other results, we clarify the structure of ) , ( τ G L and characterize amenab...

in this paper, we  study the arens regularity properties of module actions. we investigate some properties of topological centers of module actions ${z}^ell_{b^{**}}(a^{**})$ and  ${z}^ell_{a^{**}}(b^{**})$ with some conclusions in group algebras.