/sci/ - Science & Math

>>12003870
>>12004683
here's the page excerpt that calculates up to n=4, I can't quite tell if it agrees with >>12004430 , would be interesting if someone knows

[math]a[/math] and [math]*[/math] are the involutions I mentioned above:

[math]\left(\mathbf{x}_{1} \wedge \mathbf{x}_{2} \wedge \ldots \wedge \mathbf{x}_{k}\right)^{*}=(-1)^{k} \mathbf{x}_{k} \wedge \mathbf{x}_{k-1} \wedge \ldots \wedge \mathbf{x}_{1}[/math]

[math]a\left(\mathbf{x}_{0}+\mathbf{x}_{1}\right)=\mathbf{x}_{0}-\mathbf{x}_{1}[/math]

I think [math]\mathbf{x}_1[/math] is the part of the tensor with an odd length, but if someone knows if I'm understanding the [math]\mathbb{Z}_2[/math] grading wrong tell me

[math]\text{CL}_n[/math] with capital L is the twisted Clifford group I mentioned, Wikipedia also calls it the Lipschitz group, while [math]\text{Cl}_n[/math] with lowercase l is the Clifford algebra.