%0 Journal Article %T C*-algebras on r-discrete Abelian Groupoids %J Journal of Sciences, Islamic Republic of Iran %I University of Tehran %Z 1016-1104 %A Myrnouri, H. %D 2017 %\ 04/01/2017 %V 28 %N 2 %P 169-174 %! C*-algebras on r-discrete Abelian Groupoids %K Decomposable groupoid %K Abelian groupoid %K Dual groupoid %K Eigen-functional %R %X We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study the norm-one eigenvectors of corresponding full C*-algebra instead of the multiplicative functionals (spectrum) which have norm-one in the abelian group case.   %U https://jsciences.ut.ac.ir/article_60753_501ae04fc0e5201548f00cf39abfe65e.pdf