广义仿射李代数上的非交换Poisson代数结构

佟洁, 靳全勤

数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 561-570.

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数学学报 ›› 2011, Vol. 54 ›› Issue (4) : 561-570. DOI: 10.12386/A2011sxxb0057
论文

广义仿射李代数上的非交换Poisson代数结构

    佟洁, 靳全勤
作者信息 +

Non-commutative Poisson Algebra Structures on Extended Affine Lie Algebras

    Jie TONG, Quan Qin JIN
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文章历史 +

摘要

非交换的Poisson代数同时具有(未必交换的)结合代数和李代数两种代数结构, 且结合代数和李代数之间满足所谓的Leibniz法则. 本文确定了一般广义仿射李代数上所有的Poisson代数结构.  

Abstract

Non-commutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In the paper, the non-commutative poisson algebra structures on extended affine Lie algebras are determined.  

关键词

广义仿射李代数 / Poisson代数 / Leibniz法则

Key words

extended affine Lie algebras / Poisson algebras / Leibniz law

引用本文

导出引用
佟洁, 靳全勤. 广义仿射李代数上的非交换Poisson代数结构. 数学学报, 2011, 54(4): 561-570 https://doi.org/10.12386/A2011sxxb0057
Jie TONG, Quan Qin JIN. Non-commutative Poisson Algebra Structures on Extended Affine Lie Algebras. Acta Mathematica Sinica, Chinese Series, 2011, 54(4): 561-570 https://doi.org/10.12386/A2011sxxb0057

参考文献

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[2] Allison B., Azam S., Berman S., Gao Y., Pianzola A., Extended affine Lie algebras and their root systems, Memoir. Am. Math. Soc., 1996.

[3] Kubo F., Finite-dimensional non-commutative Poisson algebras, Journal of Pure and Applied Algebra, 1996, 113: 307-314.

[4] Kubo F., Non-commutative Poisson algebra structures on affine Kac-Moody algebras, Journal of Pure and Applied Algebra, 1996, 126: 267-286.

[5] Jin Q. Q., Tong J., Poisson algebra structures on toroidal Lie algebras, Chin. Ann. Math., 2007, 28(1): 57-70 (in Chinese).

[6] Tong J., Jin Q. Q., Poisson algebra structures on toroidal Lie algebras II, J. of Math. (PRC), 2010, 30(1): 145-151.

[7] Tong J., Jin Q. Q., Poisson algebra structures on slN(CQ), Acta Mathematica Sinica, Chinese Series, 2009, 52(1): 17-32.

[8] Jin Q. Q., Tong J., Poisson algebra structures on sp2l(CQ), with nullity m, Acta Mathematica Scientia, 2007, 27B(3): 73-490.

[9] Tong J., Jin Q. Q., Poisson algebra structures on the Lie algebras son(CQ), Algebra Colloquium, 2007, 14(3): 521-536.

[10] Bourbaki N., Groupes et Algebras de Lie, Paris: Hermann, 1968.

[11] Kac V. G., Infinite Dimensional Lie Algebras, Boston: Birkh¨auser, 1983.

基金

国家自然科学基金资助项目(11071187);上海市教委科研创新资助项目(09YZ336),上海市自然科学基金资助项目

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