= Exterior-power Lie algebra representation
{title2=$x\cdot(v_1\wedge\cdots\wedge v_r)=\sum_i v_1\wedge\cdots\wedge xv_i\wedge\cdots\wedge v_r$}
A <Lie algebra representation> on $V$ induces one on each <exterior power> by acting on every factor and summing. The <tensor product of Lie algebra representations> preserves the defining alternating relations, so this descends to the quotient in every <characteristic of a field>. In <characteristic two> define the <exterior algebra> by the relations $v\wedge v=0$, rather than by dividing a tensor antisymmetrizer by $2$.
Back to article page
