呻吟 发表于 2025-3-21 18:11:29
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Basic Concepts,The key notion in the definition of Lie algebras in physics is that of the commutator (or bracket), denoted by [,]. The commutator of . and . is defined as. It satisfies the relations . The operation . is in general neither commutative nor associative.柳树;枯黄 发表于 2025-3-22 14:38:51
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Lie Groups,A set of elements ., ., ., ., forms a group . if it satisfies the following axioms:Servile 发表于 2025-3-23 00:04:55
Lie Algebras and Lie Groups,The relationship between Lie algebras and Lie groups is of great importance. Let the Lie algebra be . and the corresponding Lie group .. The relation is . where the ..’s are the parameters of the group and the sum goes over the order of the group.Pathogen 发表于 2025-3-23 02:24:11
Homogeneous and Symmetric Spaces (Coset Spaces),Consider an algebra . with elements ..(. = 1, ., .), . ∋ .., and its associated group . obtained from . by exponentiation (.), ., where .. are the parameters of the group.athlete’s-foot 发表于 2025-3-23 06:20:53
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