page_title: Glossary of Lie groups and Lie algebras
section_title: J
hierarchical_section_title: Glossary of Lie groups and Lie algebras / J
caption_attribution_description: English: Carl Gustav Jacob Jacobi was not only a great German mathematician but also considered by many as the most inspiring teacher of his time. Deutsch: Carl Gustav Jacob Jacobi
context_page_description: This is a glossary for the terminology applied in the mathematical theories of Lie groups and Lie algebras. Because of the lack of other options, the glossary also includes some generalizations such as quantum group.
  Notations:
  Throughout the glossary, denotes the inner product of a Euclidean space E and denotes the rescaled inner product
context_section_description: Jacobi identity
  1.  Carl Gustav Jacob Jacobi (1804 – 1851), a German mathematician.
  2.  Given a binary operation , the Jacobi identity states: [[x, y], z] + [[y, z], x] + [[z, x], y] = 0.
caption: Carl Gustav Jacob Jacobi
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