Abstract
We are defining the trigonometric Lie subalgebras in\(\bar X_\infty = \bar A_\infty (\bar B_\infty ,\bar C_\infty ,\bar D_\infty )\) which are the natural generalization of the well known Sin-Lie algebra. The embedding formulas into\(\bar X_\infty \) are introduced. These algebras can be considered as some Lie algebras of quantum tori. An irreducible representation ofA, B series of trigonometric Lie algebras is constructed. Special cases of the trigonometric Lie factor algebras, which can be considered as a quantum (preserving Lie algebra structure) deformation of the Kac-Moody algebras are considered.
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Communicated by N. Yu. Reshetikhin
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Golenishcheva-Kutuzova, M., Lebedev, D. Vertex operator representation of some quantum tori Lie algebras. Commun.Math. Phys. 148, 403–416 (1992). https://doi.org/10.1007/BF02100868
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DOI: https://doi.org/10.1007/BF02100868