2009/04/07 by Nawata, Norio
#11R11 (Secondary) #46L05 (Primary) 11D09 #FOS: Mathematics #Number Theory (math.NT) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.0904.1085
Noncommutative tori with real multiplication are the irrational rotation algebras that have special equivalence bimodules. Y. Manin proposed the use of noncommutative tori with real multiplication as a geometric framework for the study of abelian class field theory of real quadratic fields. In this paper, we consider the Cuntz-Pimsner algebras constructed by special equivalence bimodules of irrational rotation algebras. We shall show that associated C^*-algebras are simple and purely infinite. We compute the K-groups of associated C^*-algebras and show that these algebras are related to the solutions of Pell's equation and the unit groups of real quadratic fields. We consider the Morita equivalent classes of associated C^*-algebras.