advanced_tools:group_theory:lie_algebras
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advanced_tools:group_theory:lie_algebras [2018/04/08 12:09] jakobadmin [Intuitive] |
advanced_tools:group_theory:lie_algebras [2018/04/08 12:13] jakobadmin [Abstract] |
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| <tabbox Intuitive> | <tabbox Intuitive> | ||
| - | The Lie algebra consists of infinitesimally small transformations and describes symmetries. Since arbitrarily large continuous | + | 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. |
| - | 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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| <WRAP tip> The natural product of a Lie algebra is not ordinary matrix multiplication, but the Lie bracket.</WRAP> | <WRAP tip> The natural product of a Lie algebra is not ordinary matrix multiplication, but the Lie bracket.</WRAP> | ||
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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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| <tabbox Abstract> | <tabbox Abstract> | ||
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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 |}} | ||
advanced_tools/group_theory/lie_algebras.txt · Last modified: 2023/03/29 17:40 by 132.76.61.54
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