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Minimal projective resolutions
Author(s):
E.
L.
Green;
Ø.
Solberg;
D.
Zacharia
Journal:
Trans. Amer. Math. Soc.
353
(2001),
2915-2939.
MSC (2000):
Primary 16E05, 18G10;
Secondary 16P10
Posted:
March 8, 2001
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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  -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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Additional Information:
E.
L.
Green
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
Email:
green@math.vt.edu
Ø.
Solberg
Affiliation:
Institutt for matematiske fag, NTNU, Lade, N--7491 Trondheim, Norway
Email:
oyvinso@math.ntnu.no
D.
Zacharia
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, New York 13244
Email:
zacharia@mailbox.syr.edu
DOI:
10.1090/S0002-9947-01-02687-3
PII:
S 0002-9947(01)02687-3
Keywords:
Projective resolutions,
finite dimensional and graded algebras
Received by editor(s):
September 21, 1998
Received by editor(s) in revised form:
January 3, 2000
Posted:
March 8, 2001
Additional Notes:
Partially supported by a grant from the NSA
Partially supported by NRF, the Norwegian Research Council
Dedicated:
Dedicated to Helmut Lenzing for his 60th birthday
Copyright of article:
Copyright
2001,
American Mathematical Society
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