Pointwise version of contractibility over group algebras and its applications (Q343460)

The author considers the concept of pointwise contractibility over semigroups and proves a relation between pointwise contractibility of a semigroup and its semigroup algebra. He shows that for a discrete group \(G\), if \(\ell^1(G)\) is pointwise contractible, then \(G\) is a periodic group. Also, necessary and sufficient conditions for the class of Munn algebras to be pointwise contractible are presented. Finally, these results are applied to semigroups and some necessary conditions for a semigroup algebra to be pointwise contractible are obtained.