Homological algebra for the representation Green functor for abelian groups
Author:
Joana Ventura
Journal:
Trans. Amer. Math. Soc. 357 (2005), 22532289
MSC (2000):
Primary 55P91, 18G10
Published electronically:
May 10, 2004
MathSciNet review:
2140440
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Abstract: In this paper we compute some derived functors of the internal homomorphism functor in the category of modules over the representation Green functor. This internal homomorphism functor is the left adjoint of the box product. When the group is a cyclic group, we construct a projective resolution of the module fixed point functor, and that allows a direct computation of the graded Green functor . When the group is , we can still build a projective resolution, but we do not have explicit formulas for the differentials. The resolution is built from long exact sequences of projective modules over the representation functor for the subgroups of by using exact functors between these categories of modules. This induces a filtration which gives a spectral sequence which converges to the desired functors.
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Additional Information
Joana Ventura
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049001 Lisboa, Portugal
Email:
jventura@math.ist.utl.pt
DOI:
http://dx.doi.org/10.1090/S0002994704035664
PII:
S 00029947(04)035664
Received by editor(s):
August 22, 2003
Published electronically:
May 10, 2004
Additional Notes:
The author was partially supported by FCT grant Praxis XXI/BD/11357/97 and a one year research grant from Calouste Gulbenkian Foundation
Article copyright:
© Copyright 2004
American Mathematical Society
