TY - JOUR
T1 - Minimal projective resolutions
AU - Green, E. L.
AU - Solberg,
AU - Zacharia, D.
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2001
Y1 - 2001
N2 - In this paper, we present an algorithmic method for computing a protective 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 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.
AB - In this paper, we present an algorithmic method for computing a protective 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 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.
KW - Finite dimensional and graded algebras
KW - Projective resolutions
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U2 - 10.1090/s0002-9947-01-02687-3
DO - 10.1090/s0002-9947-01-02687-3
M3 - Article
AN - SCOPUS:23044526677
VL - 353
SP - 2915
EP - 2939
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 7
ER -