# Module of covariants

In algebra, given an algebraic group *G*, a *G*-module *M* and a *G*-algebra *A*, all over a field *k*, the **module of covariants** of type *M* is the
-module

where
refers to taking the elements fixed by the action of *G*; thus,
is the ring of invariants of *A*.

## See also

## 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. 352–362, 1995.

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