Woit · §5.4 Lie algebra representations
英文原文
The source names the identity obtained from the adjoint representation and states it as an axiom for abstract Lie algebras.
原文相关讨论摘录
This is called the Jacobi identity. It could have been more simply derived as an identity about matrix multiplication, but here we see that it is true for a more abstract reason, reflecting the existence of the adjoint representation. It can be written in other forms, rearranging terms using antisymmetry of the commutator, with one example the sum of cyclic permutations
来源与版本
正文：英文原文
来源版本：2025-10-20
原文位置：§5.4；PDF 页 75；印刷页 58
处理记录：PDF 文字层提取；MinerU OCR；AI 辅助转录对照
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来源 PDF SHA-256：5a1941b2443b54d5db3d055f1e5ba390429b7a728475258017aaac87ee85a837
英文原文
The source names the identity obtained from the adjoint representation and states it as an axiom for abstract Lie algebras.
原文定义摘录
- Jacobi identity:
来源与版本
正文：英文原文
来源版本：2025-10-20
原文位置：§5.4；PDF 页 75；印刷页 58
处理记录：PDF 文字层提取；MinerU OCR；AI 辅助转录对照
核对状态：AI 辅助转录核对，未作人工审阅或数学审稿
来源 PDF SHA-256：5a1941b2443b54d5db3d055f1e5ba390429b7a728475258017aaac87ee85a837