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An Approach by Representation of Algebras for Decoherence-Free Subspaces

The aim of this paper is to present a general algebraic formulation for the Decoherence-Free Subspaces (DFSs). For this purpose, we initially generalize some results of Pauli and Artin about semisimple algebras. Then we derive orthogonality theorems for algebras analogous to finite groups. In order to build the DFSs we consider the tensor product of Clifford algebras and left minimal ideals. Furthermore, we show that standard applications of group theory in quantum chemistry can be obtained in our formalism. Advantages and some perspectives are also discussed.