The classification question for Leavitt path algebras - Mathematics > Rings and AlgebrasReport as inadecuate




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Abstract: We prove an algebraic version of the Gauge-Invariant Uniqueness Theorem, aresult which gives information about the injectivity of certain homomorphismsbetween ${\mathbb Z}$-graded algebras. As our main application of this theorem,we obtain isomorphisms between the Leavitt path algebras of specified graphs.From these isomorphisms we are able to achieve two ends. First, we show thatthe $K 0$ groups of various sets of purely infinite simple Leavitt pathalgebras, together with the position of the identity element in $K 0$,classifies the algebras in these sets up to isomorphism. Second, we show thatthe isomorphism between matrix rings over the classical Leavitt algebras,established previously using number-theoretic methods, can be reobtained viaappropriate isomorphisms between Leavitt path algebras.



Author: G. Abrams, P. N. Ánh, A. Louly, E. Pardo

Source: https://arxiv.org/







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