TY - JOUR ID - 60753 TI - C*-algebras on r-discrete Abelian Groupoids JO - Journal of Sciences, Islamic Republic of Iran JA - JSCIENCES LA - en SN - 1016-1104 AU - Myrnouri, H. AD - Department of Mathematics, Faculty of Mathematical Sciences, Lahijan Branch of Islamic Azad University, Guilan, Islamic Republic of Iran Y1 - 2017 PY - 2017 VL - 28 IS - 2 SP - 169 EP - 174 KW - Decomposable groupoid KW - Abelian groupoid KW - Dual groupoid KW - Eigen-functional DO - N2 - 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.   UR - https://jsciences.ut.ac.ir/article_60753.html L1 - https://jsciences.ut.ac.ir/article_60753_501ae04fc0e5201548f00cf39abfe65e.pdf ER -