Chpaters 1-3 Flashcards
Define a group
Define an abelian group
Define a subgroup
Define normal subgroup
Define a simple group
Define the centre and centraliser of a group
Define a group homomorphism
Define the image and kernel
Define the semi-direct product of groups
Define a manifold
What is a d-dimensional embedded submanifold?
Construction of embedded submanifolds
Define a smooth map
Define a Lie group
Define an embedded Lie subgroup
An embedded Lie sugbroup of a Lie group G is a subgroup of G endowed with topology and smooth structure that makes it a Lie group and an embedded submanifold of G.
Define a Lie subgroup
A Lie sugbroup of a Lie group G is a subgroup of G endowed with topology and smooth structure that makes it a Lie group and an immersed submanifold of G.
Define a derivation at p
Define the vector field on a manifold
Define a vector field on a manifold
Define the Lie bracket
Define differential at p
Define immersed submanifold
Define a Lie subgroup
Define a left-invariant vector field and the Lie algebra of a Lie group
