Geodesic
Weighted Leavitt path algebras -- an overview
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 40, Tome 531 (2024), pp. 157-237

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Weighted Leavitt path algebras were introduced in 2013 by Roozbeh Hazrat. These algebras generalise simultaneously the usual Leavitt path algebras and William Leavitt's algebras $L(m,n)$. In this paper we try to give an overview of what is known about the weighted Leavitt path algebras. We also prove some new results (in particular on the graded $\mathrm{K}$-theory of weighted Leavitt path algebras) and mention open problems. 
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     author = {R. Preusser},
     title = {Weighted {Leavitt} path algebras -- an overview},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_531_a10/}
}
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R. Preusser. Weighted Leavitt path algebras -- an overview. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 40, Tome 531 (2024), pp. 157-237. http://geodesic.mathdoc.fr/item/ZNSL_2024_531_a10/