Leavitt path algebras satisfying a polynomial identity

2014/08/17 by Bell, Jason, Lenagan, T. H., Rangaswamy, Kulumani M. · 1 citation
#16G20 #16R99 #16S99 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1408.3808

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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• Quivers with Polynomial Identities

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