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advanced_tools:group_theory:lie_algebras [2018/04/08 12:13] jakobadmin [Concrete] |
advanced_tools:group_theory:lie_algebras [2018/04/08 13:00] jakobadmin [Intuitive] |
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- | The Lie algebras consist of infinitesimally small transformations and are used in physics to describe [[basic_tools:symmetry|symmetries]]. Since arbitrarily large continuous transformations can be built up from tiny ones, almost everything that is important about continuous transformations is encoded in the infinitesimal ones. | + | The Lie algebras consist of infinitesimally small transformations and are used in physics to describe [[basic_tools:symmetry|symmetries]]. Since arbitrarily large continuous transformations can be built up from tiny ones, almost everything that is important about continuous transformations is encoded in the infinitesimal ones. |
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+ | Formulated differently, Lie algebras describe infinitesimal symmetries. | ||
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+ | * [[http://jakobschwichtenberg.com/lie-algebra-able-describe-group/|How is a Lie Algebra able to describe a Group?]] | ||
+ | * [[http://www.wetsavannaanimals.net/wordpress/what-information-about-a-lie-group-is-not-encoded-in-its-lie-algebra/|What Information About a Lie Group is Not Encoded in its Lie Algebra?]] | ||
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{{ :advanced_tools:group_theory:adjoint.png?nolink |}} | {{ :advanced_tools:group_theory:adjoint.png?nolink |}} |