Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Invariant-free representations of augmented rings


Author: Peter M. Curran
Journal: Trans. Amer. Math. Soc. 230 (1977), 313-319
MSC: Primary 16A62; Secondary 18H15
MathSciNet review: 0444710
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \Gamma $ be an augmented ring in the sense of Cartan-Eilenberg, and let there be given a representation of $ \Gamma $ in $ {\text{End}_k}\;A$, where A is a finite dimensional vector space over the field k. We show that all cohomology of $ \Gamma $ in A is trivial if there are no invariants in A under the action of a suitable commutative subring of $ \Gamma $. This generalizes a previous result of the author for group cohomology, and is applied to obtain sufficient conditions for the vanishing of the cohomology of Lie algebras and associative algebras.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16A62, 18H15

Retrieve articles in all journals with MSC: 16A62, 18H15


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0444710-0
Keywords: Augmented ring, cohomology of Lie algebras, cohomology of associative algebras, extensions of Lie algebras, extensions of associative algebras
Article copyright: © Copyright 1977 American Mathematical Society