Leibniz Central Extensions on Some Infinite-Dimensional Lie Algebras

Abstract

In this paper, all one-dimensional Leibniz central extensions on the algebras of differential operators over C[t, t ⁻¹] and C((t)), as well as on the quantum 2-torus, the Virasoro-like algebra and its q-analog are studied. We determine all nontrivial Leibniz 2-cocycles on these infinite dimensional Lie algebras.

Key Words:

• Leibniz 2-cocycle
• Witt algebra
• Quantum 2-torus
• Differential operators algebra
• Virasoro-like algebra
• q-Analog

Mathematics Subject Classification:

• 17A32
• 17B99
• 18G60

Acknowledgments

The authors would like to express their sincere gratitude to Professor Yun Gao for his helpful comments and valuable suggestions. Project was supported by the NNSF of China (Grant No. 10271047, Grant No. 19731004), the TRAPOYT and the FUKT and the SFUDP from the MOE of China, the SYVPST from the SSTC, and the Shanghai Priority Academic Discipline from the SEC.

Notes

^#Communicated by B. Allison.