一类扩张仿射李代数上的非交换Poisson代数

向红, 曾波, 曹佑安

数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 479-490.

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PDF(460 KB)
数学学报 ›› 2015, Vol. 58 ›› Issue (3) : 479-490. DOI: 10.12386/A2015sxxb0049
论文

一类扩张仿射李代数上的非交换Poisson代数

    向红, 曾波, 曹佑安
作者信息 +

Non-Commutative Poisson Algebra Structures on Some Extended Affine Lie Algebras

    Hong XIANG, Bo ZENG, You An CAO
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文章历史 +

摘要

讨论了以量子环面为坐标代数,零度vA型扩张仿射李代数上的非交换的Poisson代数,证明了它的导出李子代数上的结合乘积是平凡的.同时,给出了标度元素的结合积的形式.

Abstract

We determine the non-commutative Poisson algebra structures on the extended affine Lie algebras of type A with nullity v whose coordinate algebra is the quantum torus. It is shown that the associative products on the derived Lie subalgebras are trivial, and the associative products of the scaling elements are described as well.

关键词

扩张仿射李代数 / Poisson代数 / 量子环面 / Leibniz法则

Key words

extended affine Lie algebra / Poisson algebra / quantum torus / Leibniz law

引用本文

导出引用
向红, 曾波, 曹佑安. 一类扩张仿射李代数上的非交换Poisson代数. 数学学报, 2015, 58(3): 479-490 https://doi.org/10.12386/A2015sxxb0049
Hong XIANG, Bo ZENG, You An CAO. Non-Commutative Poisson Algebra Structures on Some Extended Affine Lie Algebras. Acta Mathematica Sinica, Chinese Series, 2015, 58(3): 479-490 https://doi.org/10.12386/A2015sxxb0049

参考文献

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[4] Jin Q. Q., Tong J., Poisson algebra structures on sp2l(CQ) with nullity m, Acta Math. Scientia, 2007, 27B(3): 473-490.

[5] Kubo F., Finite-dimensional non-commutative Poisson algebra, J. Pure Appl. Algebra, 1996, 113: 307-314.

[6] Kubo F., Non-commutative Poisson algebra structures on affine Kac-Moody algebras, J. Pure Appl. Algebra, 1998, 126: 276-286.

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

[8] Tong J., Jin Q. Q., Non-commutative Poisson algebra structures on Lie algebra slN(CQ), Acta Math. Sinica, Chinese Series, 2009, 52(1): 17-32.

基金

国家自然科学基金资助项目(11171202);湖南省教育厅一般资助项目(10C1260)

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