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Representations of algebras as universal localizations

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Maths_Ranicki_Representations of algebras as universal localizations.pdf (138.5Kb)
Date
01/01/2004
Author
Ranicki, Andrew
Schofield, A.
Neeman, A.
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Abstract
Given a presentation of a finitely presented group, there is a natural way to represent the group as the fundamental group of a 2-complex. The first part of this paper demonstrates one possible way to represent a finitely presented algebra $S$ in a similarly compact form. From a presentation of the algebra, we construct a quiver with relations whose path algebra is finite dimensional. When we adjoin inverses to some of the arrows in the quiver, we show that the path algebra of the new quiver with relations is $M_n(S)$ where $n$ is the number of vertices in our quiver. The slogan would be that every finitely presented algebra is Morita equivalent to a universal localization of a finite dimensional algebra.
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http://journals.cambridge.org/download.php?file=/PSP/PSP136_01/S030500410300700Xa.pdf&code=abe5612732bee7e8215d621ee092fd38

http://dx.doi.org/10.1017/S030500410300700X

http://hdl.handle.net/1842/3038
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