Abstract
For a graph E, we introduce the notion of an extended E-algebraic branching system, generalising the notion of an E-algebraic branching system introduced by Gonçalves and Royer. We classify the extended E-algebraic branching systems and show that they induce modules for the corresponding Leavitt path algebra L(E). Among these modules we find a class of nonsimple modules whose endomorphism rings are fields.
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Acknowledgements
I would like to thank Daniel Gonçalves for encouraging me to write this paper. I would also like to thank Tran Giang Nam, who asked me if I know any modules over Leavitt path algebras that are counter-examples to the converse of Schur’s lemma. This question led to Sect. 6.
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Preusser, R. Modules for Leavitt Path Algebras via Extended Algebraic Branching Systems. Bull Braz Math Soc, New Series 54, 18 (2023). https://doi.org/10.1007/s00574-023-00333-z
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DOI: https://doi.org/10.1007/s00574-023-00333-z