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Note on Complete Cohomology of a Quasi-Frobenius Algebra

Published online by Cambridge University Press:  22 January 2016

Tadasi Nakayama
Tadasi Nakayama*
Affiliation:
Nagoya University
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Let A be a quasi-Frobenius algebra over a field K. A has a complete (co)homology theory which may be established upon an augmented acyclic projective complex, i.e. a commutative diagram

of A-double-modules with exact horizontal row, projective Xp, and with epimorphic resp. monomorphic ε and t. Negative-dimensional cohomology groups, over an A-double-module, are expected to be in close relationship with (ordinary positive-dimensional) homology groups.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 13 , June 1958 , pp. 115 - 121
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1958

References

[1] Cartan, H., Séminaire de topologie algébrique, 1950–51.Google Scholar
[2] Eilenberg, H. Cartan-S., Homological Algebra, Princeton 1956.Google Scholar
[3] Nakayama, T., On the complete cohomology theory of Frobenius algebras, Osaka Math. J., 9 (1957), 165–187.Google Scholar