Module derivation problem for inverse semigroups

作者：Bagha Davood Ebrahimi; Amini Massoud^*

来源：Semigroup Forum, 2012, 85(3): 525-532.

DOI：10.1007/s00233-012-9431-1

• Banach modules
• Module amenability
• Derivation problem
• Semigroup algebra
• Inverse semigroup

The derivation problem for a locally compact group G asserts that each bounded derivation from L (1)(G) to L (1)(G) is implemented by an element of M(G). Recently a simple proof of this result was announced. We show that basically the same argument with some extra manipulations with idempotents solves the module derivation problem for inverse semigroups, asserting that for an inverse semigroup S with set of idempotents E and maximal group homomorphic image G (S) , if E acts on S trivially from the left and by multiplication from the right, any bounded module derivation from a%26quot;%26quot; (1)(S) to a%26quot;%26quot; (1)(G (S) ) is inner.

• 出版日期2012-12