形变bms3代数上的左对称代数结构

余意, 孙建才

数学学报 ›› 2021, Vol. 64 ›› Issue (6) : 947-958.

PDF(405 KB)
PDF(405 KB)
数学学报 ›› 2021, Vol. 64 ›› Issue (6) : 947-958. DOI: 10.12386/A2021sxxb0078
论文

形变bms3代数上的左对称代数结构

    余意, 孙建才
作者信息 +

Left-symmetric Algebra Structures on the Deformed bms3 Algebra

    Yi YU Jian, Cai SUN
Author information +
文章历史 +

摘要

本文主要通过对具有一定自然阶化条件的形变bms3代数上的相容左对称代数结构的分类讨论,刻画了形变bms3代数的相容左对称代数结构.

Abstract

We mainly determine the compatible left-symmetric algebra structures on the deformed bms3 algebra with some natural grading conditions by classified the compatible left-symmetric algebra structures on the deformed bms3 algebra.

关键词

形变bms3代数 / 左对称代数 / 李代数

Key words

the deformed bms3 algebra / left-symmetric algebra / Lie algebra

引用本文

导出引用
余意, 孙建才. 形变bms3代数上的左对称代数结构. 数学学报, 2021, 64(6): 947-958 https://doi.org/10.12386/A2021sxxb0078
Yi YU Jian, Cai SUN. Left-symmetric Algebra Structures on the Deformed bms3 Algebra. Acta Mathematica Sinica, Chinese Series, 2021, 64(6): 947-958 https://doi.org/10.12386/A2021sxxb0078

参考文献

[1] Andrada A., Salamon S., Complex product structure on Lie algebras, Forum Math., 2005, 17:261-295.
[2] Bai C. M., A further study on non-abelian phase spaces:Left-symmetric algebraic approach and related geometry, Rev. Math. Phys., 2006, 18:545-564.
[3] Bordemann M., Generalized Lax pairs, the modified classical Yang-Baxter equation, and affine geometry of Lie groups, Comm. Math. Phys., 1990, 135:201-216.
[4] Burde D., Simple left-symmetric algebras with solvable Lie algebra, Manuscripta Math., 1998, 95:397-411.
[5] Burde D., Left-symmetric algebras, or pre-Lie algebras in geometry and physics, Cent. Eur. J. Math., 2006, 4:323-357.
[6] Caroca R., Concha P., Rodíguez E., et al., Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra, European Phys. J. C, 2018, 78, Article No. 262.
[7] Cayley A., On the theory of the analytic forms called trees, In:Collected Mathematical Papers of Arthur Cayley, Cambridge University Press, Cambridge, 1890, 3:242-246.
[8] Chapoton F., Classification of some simple graded pre-Lie algebras of growth one, Commun. Algebra, 2004, 32:243-251.
[9] Chen H. J., Li J. B., Left-symmetric algebra structures on the W-algebra W (2, 2), Lin. Alg. Appl., 2012, 437:1821-1834.
[10] Chen H. J., Li J. B., Left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra, Sci. China Math., 2014, 57:469-476.
[11] Dardié J., Médina A., Algèbres de Lie kählériennes et double extension, J. Algebra, 1996, 185:774-795.
[12] Dardié J., Médina A., Double extension symplectique d'un groupe de Lie symplectique, Adv. Math., 1996, 117:208-227.
[13] Diatta A., Médina, Classcal Yang-Baxter equation and left invariant affine geometry on Lie groups, Manuscripta Math., 2004, 114:477-486.
[14] Etingof P., Soloviev A., Quantization of geometric classical r-matrices, Math. Res. Lett., 1999, 6:223-228.
[15] Gerstenhaber M., The cohomology structure of an associative ring, Ann. Math., 1963, 78:267-288.
[16] Golubchik I. Z., Sokolov V. V., Generalized operator Yang-Baxter equations, integrable ODEs and nonassociative algebras, J. Nonlinear Math. Phys., 2000, 7:184-197.
[17] Kim H., Complete left-invariant affine structures on nilpotent Lie groups, J. Diff. Geom., 1986, 24:373-394.
[18] Kong X. L., Bai C. M., Left-symmetric superalgebra structures on the super-Virasoro algebras, Pacific J. Math., 2008, 235:43-55.
[19] Kong X. L., Chen H. J., Bai C. M., Classification of graded left-symmetric algebra structures on the Witt and Virasoro algebras, Intern. J. Math., 2011, 22:201-222.
[20] Koszul J., Domaines bornés homogènes et orbites de groups de transformations affines, Bull. Soc. Math. France, 1961, 89:515-533.
[21] Kupershmidt B. A., On the nature of the Virasoro algebra, J. Nonlinear Math. Phys., 1999, 6:222-245.
[22] Kupershmidt B. A., Non-abelian phase spaces, J. Phys., 1994, 27:2801-2809.
[23] Liu X. W., Guo X. Q., Bian D. P., A note on the left-symmetric algebraic structures of the Witt algebra, Linear Multilinear Algebra, 2017, 65:1793-1804.
[24] Liu X. W., Bian D. P., Guo X. Q., Left-symmetric superalgebra structures on the N=2 superconformal algebras, Commun. Algebra, 2018, 46:929-941.
[25] Tang X. M., Bai C., A class of non-graded left-symmetric algebraic structures on the Witt algebra, Math. Nachr., 2012, 285:922-935.
[26] Vinberg E. B., Convex homogeneous cones, Transl. of Moscow Math. Soc., 1963, 12:340-403.

基金

国家自然科学基金资助项目(11671247,11931009)

PDF(405 KB)

Accesses

Citation

Detail

段落导航
相关文章

/