完备化Witt代数的最高权表示

梁俊平, 范广哲

数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 353-358.

PDF(426 KB)
PDF(426 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 353-358. DOI: 10.12386/A2015sxxb0035
论文

完备化Witt代数的最高权表示

    梁俊平1, 范广哲2
作者信息 +

Highest Weight Representations of the Completed Witt Algebra

    Jun Ping LIANG1, Guang Zhe FAN2
Author information +
文章历史 +

摘要

本文讨论了完备化Witt 李代数Verma 模的不可约性,并利用其子代数给出了Virasoro 代数的两类不可约非权模的实现,得到了一些有趣的组合恒等式.

Abstract

We investigate the irreducibility of Verma modules over the completed Witt algebra. By embedding the Virasoro algebra into the completed Witt algebra, we give realizations of two classes of irreducible non-weight Virasoro-modules. We also obtain some interesting combinatorial identities.

关键词

完备化 Witt 代数 / Virasoro 代数 / 最高权模 / 不可约表示 / 组合恒等式

Key words

completed Witt algebra / the Virasoro algebra / highest weight modules / irreducible representations / combinatorial identities

引用本文

导出引用
梁俊平, 范广哲. 完备化Witt代数的最高权表示. 数学学报, 2015, 58(3): 353-358 https://doi.org/10.12386/A2015sxxb0035
Jun Ping LIANG, Guang Zhe FAN. Highest Weight Representations of the Completed Witt Algebra. Acta Mathematica Sinica, Chinese Series, 2015, 58(3): 353-358 https://doi.org/10.12386/A2015sxxb0035

参考文献

[1] Hu N., Shen G., On the representations of the Witt algebra, Chin. Sci. Bull., 1998, 43(3): 189-192.

[2] Kac V., Raina A., Bombay Lectures on Highest Weight Representations of Infinite-Dimensional Lie Algebras, Advanced Series in Mathematical Physics, World Scientific Publishing Co., Inc, Teaneck, NJ, 1987.

[3] Lu R., Zhao K., Irreducible Virasoro modules from irreducibleWeyl modules, J. Algebra, 2014, 414: 271-287.

[4] Rudakov A. N., Automorphism groups of infinite-dimensional simple Lie algebras (Russian), Izv. Akda. Nauk SSSR Ser. Mat., 1969, 33: 748-764.

[5] Song G., Su Y., Lie bialgebras of generalized Witt type, Sci. China. Ser. A, 2006, 49(4): 533-544.

[6] Su Y., Xu X., Zhang H., Derivation-simple algebras and the structures of Lie algebras of Witt type, J. Algebra, 2000, 233: 642-662.

[7] Su Y., Zhao K., Second cohomology group of generalized Witt Lie algebras and certain representations, Comm. Algebra, 2002, 30(7): 3285-3309.

[8] Su Y., Zhou J., Some representations of nongraded Lie algebras of generalized Witt type, J. Algebra, 2001, 246: 721-738.

[9] Wu Y., Xu Y., Yuan L., Dervations and automorphism groups of complete Witt Lie algebra, Algebra Colloquium, 2012, 19(03): 581-590.

基金

国家自然科学基金资助项目(11371278, 11431010);上海市科委课题资助项目(12XD1405000); 中央高校基本科研业务费专项基金

PDF(426 KB)

Accesses

Citation

Detail

段落导航
相关文章

/