Minimal projective resolutions

Authors:
E. L. Green, Ø. Solberg and D. Zacharia

Journal:
Trans. Amer. Math. Soc. **353** (2001), 2915-2939

MSC (2000):
Primary 16E05, 18G10; Secondary 16P10

DOI:
https://doi.org/10.1090/S0002-9947-01-02687-3

Published electronically:
March 8, 2001

MathSciNet review:
1828479

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-01-02687-3

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

Published electronically:
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

Article copyright:
© Copyright 2001
American Mathematical Society