Why Are Lie Groups Considered Manifolds?

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Discussion Overview

The discussion centers on the relationship between Lie groups and manifolds, specifically exploring why Lie groups are classified as manifolds. The scope includes theoretical aspects of mathematics and the definitions involved in these concepts.

Discussion Character

  • Conceptual clarification

Main Points Raised

  • One participant states that a manifold equipped with a special binary operation that satisfies the axioms of a group is a Lie group, referencing Sophus Lie's contribution.
  • Another participant asserts that this classification is true by definition.

Areas of Agreement / Disagreement

Participants appear to agree on the definition of Lie groups as manifolds, but the discussion does not explore deeper implications or alternative viewpoints.

Shaun Culver
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Why are Lie groups also manifolds?
 
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A manifold equipped with a special binary operation that satisfies the axioms of a group is a Lie group, named after Sophus Lie who discovered that binary operation.
 
It's true by definition.
 
Thank you.
 

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