Module of covariants: Difference between revisions

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In [[algebra]], given aan [[algebraic group]] ''G'', a [[group representation|''G''-module]] ''M'' and a ''G''-algebra ''A'', bothall over a [[field (mathematics)|field]] ''k'', the '''module of covariants''' of type ''M'' is the <math>A^G</math>-module

{{orphan|date=June 2014}}

In algebra, given a group ''G'', a ''G''-module ''M'' and a ''G''-algebra ''A'', both over a field ''k'', the '''module of covariants''' is the <math>A^G</math>-module

: <math>(M \otimes_k A)^G.</math>.

where <math>-^G</math> refers to taking the elements fixed by the action of ''G''; thus, <math>A^G</math> is the [[ring of invariants]] of ''A''.

== See also ==

*[[localLocal cohomology]]

== References ==

* M. Brion, ''Sur les modules de covariants'', Ann. Sci. École Norm. Sup. (4) 26 (1993), 1 21.

* M. Van den Bergh, ''Modules of covariants'', Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zurich, 1994), Birkhauser, Basel, pp.&nbsp;352–362, 1995.

[[Category:Module theory]]

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