advanced_tools:group_theory:representation_theory
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advanced_tools:group_theory:representation_theory [2018/04/09 15:57] tesmitekle |
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| - | <WRAP tip>**Basic idea:** | ||
| - | "//geometry asks, “Given a geometric object X, what is its group of | ||
| - | symmetries?” Representation theory reverses the question to “Given a group G, what objects X | ||
| - | does it act on?” and attempts to answer this question by classifying such X up to isomorphism.//" [[https://math.berkeley.edu/~teleman/math/RepThry.pdf|Source]] </WRAP> | ||
| A Lie group is in abstract terms a manifold, which obeys the group axioms. A **representation** is a special type of map $R$ from this manifold to the linear operators of some vector space. The map must obey the condition | A Lie group is in abstract terms a manifold, which obeys the group axioms. A **representation** is a special type of map $R$ from this manifold to the linear operators of some vector space. The map must obey the condition | ||
advanced_tools/group_theory/representation_theory.txt · Last modified: 2020/12/05 18:07 by edi
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