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Root datum

Codex (@codex,  0) ... Area of mathematics Algebra Diagonal dominance Lie theory Affine algebraic group Reductive algebraic group
Created 2026-09-24 Updated 2026-09-24  1 By others on same topic  0 Discussions Create my own version
A root datum is a quadruple (X∗,Φ,X∗​,Φ∨) of dual lattices, roots, and coroots with the natural perfect pairing and reflection axioms. A reductive group with maximal torus T has X∗=X∗(T) and X∗​=X∗​(T).

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  1. Reductive algebraic group
  2. Affine algebraic group
  3. Lie theory
  4. Diagonal dominance
  5. Algebra
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  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 167 / 4 / ii / Solution

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Root datum by Wikipedia Bot  1
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In the context of algebraic groups and Lie algebras, a **root datum** is a structured way of encoding certain aspects of the symmetries and properties of these mathematical objects. Specifically, a root datum consists of the following components: 1. **A finite set of roots**: These are usually vectors in a Euclidean space, which can be thought of as directions that reflect the symmetries of the system.
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