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When twist of a Leavitt path algebra is again a Leavitt path algebra
Abstract
In this paper, we study Zhang twist of Leavitt path algebra LK(E) using a graded automorphism σ induced by a graph automorphism such that the twisted algebra is a Leavitt path algebra over another graph Eσ which is a twisted graph obtained from the original graph E. We establish combinatorial connection between the graphs E and Eσ and as a consequence, we show that many ring-theoretic properties are invariant for Leavitt path algebras under the twist by σ. We also define the notion of noncommutative projective scheme for ℤ-graded algebras that coincides with the notion of noncommutative projective scheme for connected ℕ-graded algebras defined by Artin and Zhang and study it in the context of twists of Leavitt path algebras.
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BibTeX
@misc{nam2026when,
title = {{When twist of a Leavitt path algebra is again a Leavitt path algebra}},
author = {Tran Giang Nam and Ashish K Srivastava},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24836},
eprint = {2609.24836},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24836},
}
RIS
TY - UNPB
TI - When twist of a Leavitt path algebra is again a Leavitt path algebra
AU - Tran Giang Nam
AU - Ashish K Srivastava
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24836
UR - https://arxiv.org/abs/2609.24836
AB - In this paper, we study Zhang twist of Leavitt path algebra L_K(E) using a graded automorphism σ induced by a graph automorphism such that the twisted algebra is a Leavitt path algebra over another graph E_σ which is a twisted graph obtained from the original graph E. We establish combinatorial connection between the graphs E and E_σ and as a consequence, we show that many ring-theoretic properties are invariant for Leavitt path algebras under the twist by σ. We also define the notion of noncommutative projective scheme for ℤ-graded algebras that coincides with the notion of noncommutative projective scheme for connected ℕ-graded algebras defined by Artin and Zhang and study it in the context of twists of Leavitt path algebras.
ER -