A Tensor Product of Representations of Cuntz Algebras.

We introduce a nonsymmetric and associative tensor product among representations of Cuntz algebras by using embeddings. Since the tensor product of permutative representations is also a permutative representation, the decomposition of such a tensor product is unique up to unitary equivalence. We show the decomposition formulae explicitly. As an application, we show properties of concrete endomorphisms. [ABSTRACT FROM AUTHOR]