ABSTRACT

In the use of the symmetric group in quantum chemistry one frequently uses algebraic methods. Before defining the symmetric group algebra let us recall some simple algebraic notions. The Frobenius or group algebra is also closed under the operation of multiplication. A linear subspace of the group algebra which is also closed under addition, multiplication by a number and multiplication is called a subalgebra. All possible linear combinations of the group elements form a linear space which is closed under the operations of addition and multiplication by a constant. A simple algebra is a finite-dimensional algebra that contains no invariant subalgebras except itself and the zero element. The centrum of the algebra contains all those elements which commute with every element of the group algebra.