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- W1499684033 abstract "In 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." @default.
- W1499684033 created "2016-06-24" @default.
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- W1499684033 date "2007-05-31" @default.
- W1499684033 modified "2023-09-27" @default.
- W1499684033 title "Classification of quasifinite representations with nonzero central charges for type $A_1$ EALA with coordinates in quantum torus" @default.
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