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Classification of quasifinite modules with nonzero central charges for EALAs of type A with coordinates in quantum torus

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Abstract

The author first constructs a Lie algebra \( \mathfrak{L}: = \mathfrak{L}(q,w_d ) \) from rank 3 quantum torus, which is isomorphic to the core of EALAs of type A d−1 with coordinates in quantum torus C q d, and then gives the necessary and sufficient conditions for the highest weight modules to be quasifinite. Finally the irreducible ℤ-graded quasifinite \( \mathfrak{L} \)-modules with nonzero central charges are classified.

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University, Suzhou, 215006, Jiangsu, China

    Rencai Lü

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  1. Rencai Lü
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Correspondence to Rencai Lü.

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Project supported by the Post Doctorate Research Grant from the Ministry of Science and Technology of China (No. 20060390526) and the National Natural Science Foundation of China (No. 10601057).

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Lü, R. Classification of quasifinite modules with nonzero central charges for EALAs of type A with coordinates in quantum torus. Chin. Ann. Math. Ser. B 30, 129–138 (2009). https://doi.org/10.1007/s11401-008-0253-0

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  • DOI: https://doi.org/10.1007/s11401-008-0253-0

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