# SUBALGEBRAS OF A q-ANALOG FOR THE VIRASORO ALGEBRA

• Published : 2003.11.01
• 57 5

#### Abstract

We define subalgebras ${V_q}^{mZ{\times}nZ}\;of\;V_q\;where\;V_q$ are in the paper [4]. We show that the Lie algebra ${V_q}^{mZ{\times}nZ}$ is simple and maximally abelian decomposing. We may define a Lie algebra is maximally abelian decomposing, if it has a maximally abelian decomposition of it. The F-algebra automorphism group of the Laurent extension of the quantum plane is found in the paper [4], so we find the Lie automorphism group of ${V_q}^{mZ{\times}nZ}$ in this paper.

#### Keywords

simple Lie algebra;maximally abelian decomposing;algebra automorphism;Lie automorphism;isomorphism

#### References

1. J. London Math. Soc. (2) v.38 no.1 Crossed products and multiplicative analogues of Weyl algebras J.C.McConnell;J.J.Pettit https://doi.org/10.1112/jlms/s2-38.1.47
2. Commun. Korean Math. Soc. v.17 no.2 Simple Lie algebras which generalizes KPS's Lie algebras K.B.Nam;M.O.Wang https://doi.org/10.4134/CKMS.2002.17.2.237
3. Progr. Math. v.92 Representations of quantum groups at roots of 1. Operator algebras, unitary representations, enveloping algebras, and invariant theory C. De Concini;V.G.Kac
4. Topics in ring theory I.N.Herstein
5. Comm. Algebra v.22 no.10 A q-analog for the Virasoro algebra E.Kirkman;C.Procesi;L.Small
6. Contem. Math. Amer. Math. Soc. v.184 On G-Graded automorphisms of generalized Witt algebras N.Kawamoto https://doi.org/10.1090/conm/184/02118