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Please, help me with the following questions or recommend some good books.
1) We have a simply-connected nilpotent Lie group G and a lattice H in G. Let L be a Lie algebra of G. There is a one to one correspondence between L and G via exp and log maps.
a) Is it true, that to an ideal in L corresponds a normal subgroup in G?
b) If we have a normal subgroup P in G, can we find a normal subgroup in H with Lie group P?
2) What is the construction of Riemann metric on the Lie group G corresponding to its lattice H?
1) We have a simply-connected nilpotent Lie group G and a lattice H in G. Let L be a Lie algebra of G. There is a one to one correspondence between L and G via exp and log maps.
a) Is it true, that to an ideal in L corresponds a normal subgroup in G?
b) If we have a normal subgroup P in G, can we find a normal subgroup in H with Lie group P?
2) What is the construction of Riemann metric on the Lie group G corresponding to its lattice H?