| 胡志广.二维李代数的可裂表示与矩阵群作用的轨道[J].数学年刊A辑,2026,(1):67~76 |
| 二维李代数的可裂表示与矩阵群作用的轨道 |
| Splittable Representations of Two-Dimensional Lie Algebra and Orbits of Matrix Group Actions |
| Received:October 14, 2025 Revised:February 11, 2026 |
| DOI：10.16205/j.cnki.cama.2026.0006 |
| 中文关键词: 可裂表示 李代数 轨道 群作用 分层图 |
| 英文关键词:Splittable representations Lie algebras Orbits Group action Layered graphs |
| 基金项目:国家自然科学基金项目(No.12131012) |
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| 中文摘要: |
| 利用分层图, 给出二维非交换李代数可裂表示的完全分类. 作为应用, 给出矩阵群GL(n1,P)×GL(n2,P)×···×GL(ns+1,P)在Pn1×n2×Pn2×n3×···×Pns×ns+1上作用(g1X1g2?1, g2X2g3?1, ···, gsXsgs+1?1)的轨道分类和标准形. |
| 英文摘要: |
| A complete classification of the splittable representations of the two-dimensional nonabelian Lie algebra is given by layered graphs. As an application, the classification and standard forms of the orbits under the action of the matrix group GL(n1,P)×GL(n2,P)×···×GL(ns+1,P) on Pn1×n2×Pn2×n3×···×Pns×ns+1 as (g1X1g2?1, g2X2g3?1, ···, gsXsgs+1?1) are determined. |
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