Algebraic group actions and quotients - IMJ-PRG
... (i) π is G-invariant. (ii) π is affine and surjective. (iii) If U ⊂ Y is open then the natural map A(U ) −→ A(π −1 (U ))G is an isomorphism. (iv) If W1 , W2 are disjoint closed G-invariant subsets of X, then π(W1 ) and π(W2 ) are disjoint closed subsets of X. A good quotient is a categorical quotien ...
... (i) π is G-invariant. (ii) π is affine and surjective. (iii) If U ⊂ Y is open then the natural map A(U ) −→ A(π −1 (U ))G is an isomorphism. (iv) If W1 , W2 are disjoint closed G-invariant subsets of X, then π(W1 ) and π(W2 ) are disjoint closed subsets of X. A good quotient is a categorical quotien ...
Algebraic Groups
... The proof shows that R∗ is a special open set of R. In particular, R∗ is irreducible of dimension dim R∗ = dim R. 1.2. Isomorphisms and products. It follows from our definition that an algebraic group G is an affine variety with a group structure. These two structures are related in the usual way. N ...
... The proof shows that R∗ is a special open set of R. In particular, R∗ is irreducible of dimension dim R∗ = dim R. 1.2. Isomorphisms and products. It follows from our definition that an algebraic group G is an affine variety with a group structure. These two structures are related in the usual way. N ...
Topological groups and stabilizers of types
... • Definable subsets of M n have a finite decomposition into manifold-like sets called cells, resulting in a good theory of dimension. • Rich theory of definable groups (examples are complex algebraic, real algebraic groups, compact Lie groups and more): ...
... • Definable subsets of M n have a finite decomposition into manifold-like sets called cells, resulting in a good theory of dimension. • Rich theory of definable groups (examples are complex algebraic, real algebraic groups, compact Lie groups and more): ...
Study guide
... ∠ 1 and ∠ 2 are a linear pair. ∠ 2 and ∠ 3 are also a linear pair. ∠ 3 and ∠ 4 are also a linear pair. ∠ 1 and ∠ 4 are also a linear pair. To find vertical angles, look for angles formed by intersecting lines. ∠ 1 and ∠ 3 are vertical angles. ∠ 2 and ∠ 4 are also vertical angles. ...
... ∠ 1 and ∠ 2 are a linear pair. ∠ 2 and ∠ 3 are also a linear pair. ∠ 3 and ∠ 4 are also a linear pair. ∠ 1 and ∠ 4 are also a linear pair. To find vertical angles, look for angles formed by intersecting lines. ∠ 1 and ∠ 3 are vertical angles. ∠ 2 and ∠ 4 are also vertical angles. ...
