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arXiv · 1408.3808

Leavitt path algebras satisfying a polynomial identity

Jason Bell·T. H. Lenagan·Kulumani M. Rangaswamy
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Abstract

Leavitt path algebras L of an arbitrary graph E over a field K satisfying a polynomial identity are completely characterized both in graph-theoretic and algebraic terms. When E is a finite graph, L satisfying a polynomial identity is shown to be equivalent to the Gelfand-Kirillov dimension of L being at most one, though this is no longer true for infinite graphs. It is shown that, for an arbitrary graph E, the Leavitt path algebra L has Gelfand-Kirillov dimension zero if and only if E has no cycles. Likewise, L has Gelfand-Kirillov dimension one if and only if E contains at least one cycle, but no cycle in E has an exit.

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Jason Bell, T. H. Lenagan, Kulumani M. Rangaswamy. 2014-08-17. Leavitt path algebras satisfying a polynomial identity. https://arxiv.org/abs/1408.3808

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