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

V. G. Gueorguiev·A. I. Georgieva·P. P. Raychev·R. P. Roussev
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Abstract

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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BibTeXRIS

V. G. Gueorguiev, A. I. Georgieva, P. P. Raychev, R. P. Roussev. 2002-09-18. q-Analogue of $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$. https://doi.org/10.1007/bf00673835

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