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

doi:10.1007/BF00673835

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

Quantum Algebra 2015-06-26 v1 Mathematical Physics Group Theory math.MP

Authors: 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.

Keywords

quantum algebras q-analogue embedding comultiplication q-boson realization isomorphism

Cite

@article{arxiv.math/0209243,
  title  = {q-Analogue of $A_{m-1}\oplus A_{n-1}\subset A_{mn-1}$},
  author = {V. G. Gueorguiev and A. I. Georgieva and P. P. Raychev and R. P. Roussev},
  journal= {arXiv preprint arXiv:math/0209243},
  year   = {2015}
}

Comments

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

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

Abstract

Keywords

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