چكيده انگليسي :
Simplicial Cohomology of Band Semigroup Algebras Zahra Mahmoodi zahra mahmoodi@math iut ac ir September 21 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Rasoul Nasr Isfahani isfahani@cc iut ac ir Advisor Dr Sima Soltani Renani soltani@cc iut ac ir 2010 MSC Primary 16E40 43A20 Keywords Banach algebra band semigroup semilattice simplicial cohomology Abstract In this thesis we give an expanded account of simplicial triviality of the convolution algebra 1 S of a band semigroup S established by Y Choi 2012 Computing the hochschild cohomology of Banach algebras has remained a di cult task even when restricted to the class of 1 convolution algebras of semigroups Choi has shown that the simplicial cohomology of the semigroup algebra 1 S vanishes when S is a normal band that is a band S for which xaby xbay for all a b x y S However the techniques were unable to handle the case of general band semigroups We note that bands comprise a rich and interesting class of semigroups particular kinds of band have been studed both in abstract semigroup theory and also in operator theoretic settings Here we calculate all the cyclic and simplicial cohomology groups of 1 S where S is an arbitrary band semigroup More precisely we shall show the following The cyclic cohomology of 1 S is isomorphic in even degrees to the space of continuous traces on 1 S and vanishes in odd degrees
