Symmetric group - Wikipedia:
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Friday, April 28, 2017
Group action - Wikipedia
Group action - Wikipedia: "Actions of groups on vector spaces are called representations of the group."
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Wednesday, April 26, 2017
Representation of a Lie group - Wikipedia
Representation of a Lie group - Wikipedia: "If a basis for the complex vector space V is chosen, the representation can be expressed as a homomorphism into general linear group GL(n,C). This is known as a matrix representation.
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Symmetry (physics) - Wikipedia
Symmetry (physics) - Wikipedia: "A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries. Continuous symmetries can be described by Lie groups while discrete symmetries are described by finite groups (see Symmetry group).
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Tuesday, April 25, 2017
Group homomorphism - Wikipedia
Group homomorphism - Wikipedia: "Types of group homomorphism[edit]
Monomorphism
A group homomorphism that is injective (or, one-to-one); i.e., preserves distinctness.
Epimorphism
A group homomorphism that is surjective (or, onto); i.e., reaches every point in the codomain.
Isomorphism
A group homomorphism that is bijective; i.e., injective and surjective. Its inverse is also a group homomorphism. In this case, the groups G and H are called isomorphic; they differ only in the notation of their elements and are identical for all practical purposes.
Endomorphism
A homomorphism, h: G → G; the domain and codomain are the same. Also called an endomorphism of G.
Automorphism"
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Monomorphism
A group homomorphism that is injective (or, one-to-one); i.e., preserves distinctness.
Epimorphism
A group homomorphism that is surjective (or, onto); i.e., reaches every point in the codomain.
Isomorphism
A group homomorphism that is bijective; i.e., injective and surjective. Its inverse is also a group homomorphism. In this case, the groups G and H are called isomorphic; they differ only in the notation of their elements and are identical for all practical purposes.
Endomorphism
A homomorphism, h: G → G; the domain and codomain are the same. Also called an endomorphism of G.
Automorphism"
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Sunday, April 23, 2017
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