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• W2963909144 abstract "Leavitt path algebras [Formula: see text] of an arbitrary graph [Formula: see text] over a field [Formula: see text] satisfying a polynomial identity are completely characterized both in graph-theoretic and algebraic terms. When [Formula: see text] is a finite graph, [Formula: see text] satisfying a polynomial identity is shown to be equivalent to the Gelfand–Kirillov dimension of [Formula: see text] being at most one, though this is no longer true for infinite graphs. It is shown that, for an arbitrary graph [Formula: see text], the Leavitt path algebra [Formula: see text] has Gelfand–Kirillov dimension zero if and only if [Formula: see text] has no cycles. Likewise, [Formula: see text] has Gelfand–Kirillov dimension one if and only if [Formula: see text] contains at least one cycle, but no cycle in [Formula: see text] has an exit." @default.
• W2963909144 created "2019-07-30" @default.
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• W2963909144 date "2016-03-30" @default.
• W2963909144 modified "2023-09-23" @default.
• W2963909144 title "Leavitt path algebras satisfying a polynomial identity" @default.
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• W2963909144 doi "https://doi.org/10.1142/s0219498816500845" @default.
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