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arXiv · 2412.09163

Moduli of representations of Leavitt path algebras

Arnaud Brothier·Dilshan Wijesena
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Abstract

We transpose Jones' technology and the authors' C*-algebraic techniques to study representations of the Leavitt path algebra L (over an arbitrary row-finite graph) by using its quiver algebra A. We establish an equivalence of categories between certain full subcategories of Rep(A) and Rep(L) that preserves irreducibility and indecomposability. We define a dimension function on Rep(L), and for each finite dimension we provide a moduli space for the irreducible classes by transporting structures of King and Nakajima on quiver representations. Our techniques are both explicit and functorial.

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Arnaud Brothier, Dilshan Wijesena. 2024-12-12. Moduli of representations of Leavitt path algebras. https://arxiv.org/abs/2412.09163

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