Gruppe/Lineare Operation/Induzierte Operationen/Fakt

${\displaystyle {}k}$

${\displaystyle {}V}$

${\displaystyle G\times V^{k}\longrightarrow V^{k},\,(\sigma ,v_{1},\ldots ,v_{k})\longmapsto (\sigma (v_{1}),\ldots ,\sigma (v_{k})).}$

${\displaystyle {}k}$

${\displaystyle {}\bigwedge ^{k}V}$

${\displaystyle G\times \bigwedge ^{k}V\longrightarrow \bigwedge ^{k}V,}$

die durch ${\displaystyle {}v_{1}\wedge \ldots \wedge v_{k}\mapsto \sigma (v_{1})\wedge \ldots \wedge \sigma (v_{k})}$ festgelegt ist.

${\displaystyle {}{V}^{*}}$

${\displaystyle {V}^{*}\times G\longrightarrow {V}^{*},\,(f,\sigma )\longmapsto f\circ \sigma .}$