Classification of quasifinite representations with nonzero central charges for type $A_1$ EALA with coordinates in quantum torus

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dc.creatorLin, Weiqiang
dc.creatorSu, Yucai
dc.date2007-05-31
dc.date.accessioned2026-07-07T08:03:42Z
dc.date.available2026-07-07T08:03:42Z
dc.descriptionIn this paper, we first construct a Lie algebra $L$ from rank 3 quantum torus, and show that it is isomorphic to the core of EALAs of type $A_1$ with coordinates in rank 2 quantum torus. Then we construct two classes of irreducible ${\bf Z}$-graded highest weight representations, and give the necessary and sufficient conditions for these representations to be quasifinite. Next, we prove that they exhaust all the generalized highest weight irreducible ${\bf Z}$-graded quasifinite representations. As a consequence, we determine all the irreducible ${\bf Z}$-graded quasifinite representations with nonzero central charges. Finally, we construct two classes of highest weight ${\bf Z}^2$-graded quasifinite representations by using these ${\bf Z}$-graded modules.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0705.4539
dc.identifierhttp://arxiv.org/abs/0705.4539
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129672
dc.subjectQuantum Algebra
dc.subjectRepresentation Theory
dc.subject17B65, 17B68
dc.titleClassification of quasifinite representations with nonzero central charges for type $A_1$ EALA with coordinates in quantum torus
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