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

arXiv0705.4539MaRDI QIDQ6205770

Wei-Qiang Lin, Yucai Su

Publication date: 31 May 2007

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 $$-graded highest weight representations, and give the necessary and sufficient conditions for these representations to be quasifinite. Next, we prove that they exhaust all the generalized highest weight irreducible $$-graded quasifinite representations. As a consequence, we determine all the irreducible $$-graded quasifinite representations with nonzero central charges. Finally, we construct two classes of highest weight $$-graded quasifinite representations by using these $$-graded modules.

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Infinite-dimensional Lie (super)algebras (17B65)

This page was built for publication: Classification of quasifinite representations with nonzero central charges for type $A_1$ EALA with coordinates in quantum torus