G-module
Sign in to savethumb|The torus can be made an abelian group isomorphic to the product of the [[circle group. This abelian group is a Klein four-group-module, where the group acts by reflection in each of the coordinate directions (here depicted by red and blue arrows intersecting at the identity element).]]
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Encyclopedic overview
5 sectionsContents
- Definition and basics
- Examples
- Topological groups
- Notes
- References
thumb|The torus can be made an abelian group isomorphic to the product of the [[circle group. This abelian group is a Klein four-group-module, where the group acts by reflection in each of the coordinate directions (here depicted by red and blue arrows intersecting at the identity element).]]
In mathematics, given a group G, a '''G-module is an abelian group M on which G acts compatibly with the abelian group structure on M. This widely applicable notion generalizes that of a representation of . Group (co)homology provides an important set of tools for studying general G-modules.
Excerpted from Wikipedia’s “G-module” article, available under the CC BY-SA 4.0 licence.