Angular Momentum

$(x_i{p}_j-x_j{p}_i)$ Gives us the Angular Momentum matrix for an arbitrary number of dimensions. This matrix contains zeroes in the diagonal and is skew-symmetric. This allows us to simplify the representation of angular momentum in lower dimensions:

Dimentions	Representation of angular momentum
1	N/A
2	The scalar $x_2{p}_1-x_1{p}_2$ suffices
3	The vector $[x_2{p}_3-x_3{p}_2,x_3{p}_1-x_1{p}_3,x_1{p}_2-x_2{p}_3]$ suffices