## REPRESENTATIONS OF ALGEBRAS AS UNIVERSAL LOCALIZATIONS

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2002-05-03##### Author

Neeman, Amnon

Ranicki, Andrew

Schofield, Aiden

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Show full item record##### 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 Mn(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.