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# Now since the symmetric group is the group of all bijections we can think of a group action as a homomorphism from to .<ref name="ref_4bac37cc" /> | # Now since the symmetric group is the group of all bijections we can think of a group action as a homomorphism from to .<ref name="ref_4bac37cc" /> | ||
# This definition allows us to easily study the concept of a group action in the framework of category theory.<ref name="ref_4bac37cc" /> | # This definition allows us to easily study the concept of a group action in the framework of category theory.<ref name="ref_4bac37cc" /> | ||
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# The term group action or action of a group is used for the notion defined here.<ref name="ref_a45f5509">[https://groupprops.subwiki.org/wiki/Group_action Group action]</ref> | # The term group action or action of a group is used for the notion defined here.<ref name="ref_a45f5509">[https://groupprops.subwiki.org/wiki/Group_action Group action]</ref> | ||
# A group action is termed faithful if no non-identity element of the group fixes everything.<ref name="ref_a45f5509" /> | # A group action is termed faithful if no non-identity element of the group fixes everything.<ref name="ref_a45f5509" /> | ||
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===소스=== | ===소스=== | ||
<references /> | <references /> | ||
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| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q288465 Q288465] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'group'}, {'LEMMA': 'action'}] | ||
2021년 2월 17일 (수) 00:51 기준 최신판
노트
위키데이터
- ID : Q288465
말뭉치
- In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space.[1]
- A group action on a (finite-dimensional) vector space is called a representation of the group.[1]
- In other words, in a faithful group action, different elements of G induce different permutations of X .[1]
- In other words, in a faithful group action, different elements of induce different permutations of .[1]
- In a group action, a group permutes the elements of .[2]
- For a given , the set , where the group action moves , is called the group orbit of .[2]
- Historically, the first group action studied was the action of the Galois group on the roots of a polynomial.[2]
- Section 7 uses a group action by automorphisms to define the semidirect product of two groups.[3]
- There are a few questions that come up when encountering a new group action.[4]
- The first condition for a group action holds by associativity of the group, and the second condition follows from the definition of the identity element.[4]
- In other words, an equivariant map is a homomorphism with respect to the group action; it is therefore also sometimes called a G-map or G-homomorphism.[5]
- Thus a Lie group action is defined to be a smooth homomorphism from a Lie group \({G}\) to \({\textrm{Diff}(M)}\), the Lie group of diffeomorphisms of a manifold \({M}\).[5]
- Note that this function must implement a group action from the right.[6]
- OrbitStabilizerAlgorithm performs an orbit stabilizer algorithm for the group G acting with the generators gens via the generator images gens and the group action act on the element pnt .[6]
- Mathematically, an external set is the set Ω, which is endowed with the action of a group G via the group action μ.[6]
- We can formalize this notion with the concept of a group action.[7]
- Now since the symmetric group is the group of all bijections we can think of a group action as a homomorphism from to .[7]
- This definition allows us to easily study the concept of a group action in the framework of category theory.[7]
- The term group action or action of a group is used for the notion defined here.[8]
- A group action is termed faithful if no non-identity element of the group fixes everything.[8]
소스
메타데이터
위키데이터
- ID : Q288465
Spacy 패턴 목록
- [{'LOWER': 'group'}, {'LEMMA': 'action'}]