Centers of Path Algebras, Cohn and Leavitt Path Algebras
This paper is devoted to the study of the center of several types of path algebras associated to a graph E over a field K. First we consider the path algebra KE and prove that if the number of vertices is infinite then the center is zero; otherwise, it is K, except when the graph E is a cycle in which case the center is K[x], the polynomial algebra in one indeterminate. Then we compute the centers of prime Cohn and Leavitt path algebras. A lower and an upper bound for the center of a Leavitt path algebra are given by introducing the graded Baer radical for graded algebras. In the final section we describe the center of a prime graph C\(^*\)-algebra for a row-finite graph.
KeywordsPath algebra Cohn path algebra Leavitt path algebra Center Graph C\(^*\)-algebra
Mathematics Subject ClassificationPrimary 16D70 46L55
All the authors have been partially supported by the Spanish Ministerio de Economía y Competitividad and Fondos FEDER, jointly, through project MTM2013-41208-P, by the Junta de Andalucía and Fondos FEDER, jointly, through projects FQM-336 and FQM-7156, and by the Programa de becas para estudios doctorales y postdoctorales SENACYT-IFARHU, contrato no. 270-2008-407, Gobierno de Panamá. This work was done during research stays of the first and last author in the University of Málaga. Both authors would like to thank the host center for its hospitality and support.
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