The commutative core of a Leavitt path algebra
Abstract
For any unital commutative ring $R$ and for any graph $E$, we identify the commutative core of the Leavitt path algebra of $E$ with coefficients in $R$, which is a maximal commutative subalgebra of the Leavitt path algebra. Furthermore, we are able to characterize injectivity of representations which gives a generalization of the Cuntz-Krieger uniqueness theorem.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2015
- DOI:
- 10.48550/arXiv.1510.03992
- arXiv:
- arXiv:1510.03992
- Bibcode:
- 2015arXiv151003992G
- Keywords:
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- Mathematics - Rings and Algebras
- E-Print:
- 19 pages