## Topological Groups Assignment Help

A topological group can be defined as a mathematical object with a group G and topology on G such that the group G’s inverse function and binary operation are continuous functions with respect to the topology. Some of the popular properties and concepts related to topological groups are identity component, quotient topology, fundamental group, homeomorphism, uniform spaces, quotient topology, normal subgroup, factor group and isomorphism theorems.

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Lie Groups | Locally Compact Groups |

Algebraic Groups | Profinite Groups |

Topological Rings | Linear Reductive and Linear Semi-Simple Groups |

Hausdorff Topological Vector Space | P-Adic Numbers |

Lies and Engels Theorem | Cartans Criterion for Semi-Simplicity |

Invariant Differential Operators | Peter-Weyl Theory |

Poincare-Birkhoff-Witt Theorem | Universal Enveloping Algebra |

Linear Lie Groups | Bruhat Decomposition |

Group Actions on Topological Spaces | Properties of Haar Measures |

Simple and Semisimple Lie Algebras | Root Space Decomposition |

The Exponential Map | Lie Algebra of Linear Lie Groups |

Iwasawa Decomposition | Schurs Lemma |

Cartan Involution | Global Cartan Decomposition |