Another source of examples of Frobenius extensions ( and twisted versions ) are certain subalgebra pairs of Frobenius algebras, where the subalgebra is stabilized by the symmetrizing automorphism of the overalgebra.
12.
The above " N "-particle function must either be symmetrized ( in the bosonic case ) or anti-symmetrized ( in the fermionic case ) with respect to the particle numbers.
13.
The above " N "-particle function must either be symmetrized ( in the bosonic case ) or anti-symmetrized ( in the fermionic case ) with respect to the particle numbers.
14.
These are multi-indexed quantities whose suitably symmetrized ( anti-symmetrized ) parts can be related to the real and imaginary parts of the relativistic moments for the full nonlinear theory in a rather complicated manner.
15.
These are multi-indexed quantities whose suitably symmetrized ( anti-symmetrized ) parts can be related to the real and imaginary parts of the relativistic moments for the full nonlinear theory in a rather complicated manner.
16.
One can say that the dynamics of a free model is one-body reducible : the many-body wave function for fermions ( bosons ) is the anti-symmetrized ( symmetrized ) product of one-body wave functions.
17.
One can say that the dynamics of a free model is one-body reducible : the many-body wave function for fermions ( bosons ) is the anti-symmetrized ( symmetrized ) product of one-body wave functions.
18.
The Court's decision symmetrized its case law, with " Weyerhaeuser " and " Brooke Group Ltd . v . Brown & Williamson Tobacco Corp . " applying identical standards to predatory buying and predatory selling claims respectively.
19.
Here symmetrizing ( respectively anti-symmetrizing ) a symmetric function multiplies by n ! thus if n ! is invertible, such as when working a field of characteristic 0 or p > n then these yield projections when divided by n !.
20.
Here symmetrizing ( respectively anti-symmetrizing ) a symmetric function multiplies by n ! thus if n ! is invertible, such as when working a field of characteristic 0 or p > n then these yield projections when divided by n !.
