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Ashish K Srivastava

Publications and source records attributed to Ashish K Srivastava.

2 recordsLinked to original sources
arXiv2026

When twist of a Leavitt path algebra is again a Leavitt path algebra

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 $\mathbb Z$-graded algebras that coincides with the notion of noncommutative projective scheme for connected $\mathbb N$-graded algebras defined by Artin and Zhang and study it in the context of twists of Leavitt path algebras.

math.RA↗
arXiv2025

Graded Naimark's Problem for Leavitt Path Algebras

In this paper we study the graded version of Naimark's problem for Leavitt path algebras considering them as $\mathbb{Z}$-graded algebras. Several characterizations are obtained of a Leavitt path algebra $L$ of an arbitrary graph $E$ over a field $\mathbb{K}$ over which any two graded-simple modules are graded isomorphic. Such a Leavitt path algebra $L$ is shown to be graded isomorphic to the algebra of graded infinite matrices having at most finitely many non-zero entries from the ring $R$ where $R=\mathbb{K}$ or $R=\mathbb{K}[x,x^{-1}]$. Equivalently, $L$ is a graded-simple ring which is graded-semisimple, that is, $L$ is a graded direct sum of graded-isomorphic graded-simple left $L$-modules. Graphically, the graph $E$ is shown to be row-finite, downward directed and the vertex set $E^{0}$ is the hereditary saturated closure of a single vertex $v$ which is either a line point or lies on a cycle without exits. We also characterize Leavitt path algebras possessing at most countably many isomorphism classes of graded-simple left modules. Examples are constructed illustrating these results.

math.RA↗