q-Analogue of $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$

Details q-Analogue of $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$ q-Analogue of $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$

2002-09-18

arxiv.org/abs/math/0209243v1

Internat. J. Theoret. Phys. 34 (1995), no. 11, p. 2195-2204

Mathematics

Quantum Algebra

11 pages, no figures. In memory of professor R. P. Roussev

Scientific paper

A natural embedding $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$ for the corresponding quantum algebras is constructed through the appropriate comultiplication on the generators of each of the $A_{m-1}$ and $A_{n-1}$ algebras. The above embedding is proved in their $q$-boson realization by means of the isomorphism between the $\mathcal{A}_q^{-}$ (mn)$\sim {\otimes} ^n \mathcal{A}_q^{-}$(m)$\sim {\otimes}^m\mathcal{A}_q^{-}$(n) algebras.

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