Please, help me with the following questions or recommend some good books.(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Lattices in nilpotent Lie groups

Loading...

Similar Threads for Lattices nilpotent groups | Date |
---|---|

Software for drawing group lattice diagrams? | Sep 6, 2015 |

Quick question about subgroups of "odd" dihedral groups | Dec 3, 2014 |

Lie theory - sum of nilpotent ideals is nilpotent? | Feb 17, 2014 |

Question about normal subgroups/Lattice Isomorphism Theorem | Dec 23, 2013 |

Number of lattice points between y=ax+b and y=x^2? | Nov 25, 2012 |

**Physics Forums - The Fusion of Science and Community**