Minimal projective resolutions

Green, E.; Solberg, Ø.; Zacharia, D.

doi:10.1090/S0002-9947-01-02687-3

Minimal projective resolutions
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by E. L. Green, Ø. Solberg and D. Zacharia PDF

Trans. Amer. Math. Soc. 353 (2001), 2915-2939 Request permission

Abstract:

In this paper, we present an algorithmic method for computing a projective resolution of a module over an algebra over a field. If the algebra is finite dimensional, and the module is finitely generated, we have a computational way of obtaining a minimal projective resolution, maps included. This resolution turns out to be a graded resolution if our algebra and module are graded. We apply this resolution to the study of the $\operatorname {Ext}$-algebra of the algebra; namely, we present a new method for computing Yoneda products using the constructions of the resolutions. We also use our resolution to prove a case of the “no loop” conjecture.

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