2n-Weak module amenability of semigroup algebras

محورهای موضوعی : Functional analysis

K. Fallahi ¹ (Department of Mathematics, Payam Noor University of Technology, Tehran, Iran)
H. Ghahramani ² (Department of Mathematics, University of Kurdistan, P. O. Box 416, Sanandaj, Iran)

تاریخ دریافت : 1397/11/07 تاریخ پذیرش : 1398/01/26 تاریخ انتشار : 1398/05/10

کلید واژه: Banach module, module derivation, inverse semigroup, 2n-weak module amenability, semigroup algebra,

چکیده مقاله :

‎Let $S$ be an inverse semigroup with the set of idempotents $E$‎.We prove that the semigroup algebra $\ell^{1}(S)$ is always‎‎$2n$-weakly module amenable as an $\ell^{1}(E)$-module‎, ‎for any‎‎$n\in \mathbb{N}$‎, ‎where $E$ acts on $S$ trivially from the left‎‎and by multiplication from the right‎. ‎Our proof is based on a common fixed point property for semigroups‎.

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