Cyclic Cohomology Group and Cyclic Amenability of Induced Semigroup Algebras

چکیده مقاله

‎Let $S$ be a discrete semigroup with idempotent set $E$ and $T$ be a left multiplier operator on $S$‎, ‎which makes it a newly induced semigroup $S _{T}$ with idempotent set $E_T$‎. ‎In this paper while examining the properties of inducted semigroup algebra $ \ell^1({S_{T}}) $‎, ‎we show that under certain conditions for $T$‎, ‎the first cyclic cohomology groups $ \HH\CC^{1}(\ell^1(S)‎, ‎\ell^{\infty}(S))$ and $\HH\CC^{1}(\ell^1({S_{T}})‎, ‎\ell^{\infty}(S_{T})) $ are equal‎, ‎where $S$ be a monoid semigroup‎. ‎We also show in another section‎, ‎when $ S $ is a completely regular semigroup‎, ‎then the semigroup algebra $ \ell^1({S_{T}}) $ is cyclic amenable‎. ‎Finally‎, ‎by providing examples at the end of each section‎, ‎we examine the conditions raised in this paper‎.