Lie groups | Topological groups

Identity component

In mathematics, specifically group theory, the identity component of a group G refers to several closely related notions of the largest connected subgroup of G containing the identity element. In point set topology, the identity component of a topological group G is the connected component G0 of G that contains the identity element of the group. The identity path component of a topological group G is the path component of G that contains the identity element of the group. In algebraic geometry, the identity component of an algebraic group G over a field k is the identity component of the underlying topological space. The identity component of a group scheme G over a base scheme S is, roughly speaking, the group scheme G0 whose fiber over the point s of S is the connected component (Gs)0 of the fiber Gs, an algebraic group. (Wikipedia).

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20 The identity element

Sets might contain an element that can be identified as an identity element under some binary operation. Performing the operation between the identity element and any arbitrary element in the set must result in the arbitrary element. An example is the identity element for the binary opera

From playlist Abstract algebra

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From playlist Introduction to Matrices and Matrix Operations

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From playlist Matrices

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3.2.2 The Identity Matrix

3.2.2 The Identity Matrix

From playlist LAFF - Week 3

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From playlist Intro to Matrices

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21 The inverse element

A set might contain many inverse elements under some binary operation. To have such an element, this set must also contain an identity element under the binary operation in question. An element is an inverse element of another element in a set if performing the binary operation between t

From playlist Abstract algebra

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From playlist Polynomials (related content)

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From playlist Probability and Statistics

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From playlist Lie Groups and Lie Algebras

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From playlist The Sato-Tate conjecture for abelian varieties

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From playlist Abstract Algebra

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From playlist Part 3 Linear Algebra: Linear Transformations

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From playlist What is General Relativity?

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From playlist Create Minecraft Like Game In Unity - Server Side

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Related pages

Prime ideal | Lie group | Split-complex number | Klein four-group | Homotopy group | Local field | Zariski topology | Maximal torus | Topological ring | Clopen set | Automorphism | Topological group | Group (mathematics) | Identity element | Root of unity | Discrete group | Quotient group | General linear group | Finite group | Open set | Connected space | Characteristic subgroup | Mathematics | Weyl group | Totally disconnected group | Algebraic geometry | Group scheme | Group theory | Normal subgroup | Reductive group | Glossary of algebraic geometry | Scheme (mathematics) | Fiber (mathematics) | Algebraic group | P-adic number | Centralizer and normalizer | Closed set