Cyclic Cohomology Group and Cyclic Amenability of Induced Semigroup Algebras

Abstract

abstract: 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 ST with idempotent set ET . In this paper while examining the
properties of inducted semigroup algebra `1ô€€€ST , we show that under certain conditions for T, the rst cyclic
cohomology groups HC1ô€€€`1ô€€€S; `
™ô€€€S and HC1ô€€€`1ô€€€ST ; `
™ô€€€ST 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 `1ô€€€ST
is cyclic amenable. Finally, by providing examples at the end of each section, we examine the conditions raised
in this paper.