In
algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary a ...
, given an
algebraic group ''G'', a
''G''-module ''M'' and a ''G''-algebra ''A'', all over a
field
Field may refer to:
Expanses of open ground
* Field (agriculture), an area of land used for agricultural purposes
* Airfield, an aerodrome that lacks the infrastructure of an airport
* Battlefield
* Lawn, an area of mowed grass
* Meadow, a grass ...
''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
*
Local 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. 352–362, 1995.
Module theory
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