288517
Let G be a Lie group and H its Cartan subgroup which admits a linear representation in a vector space V. A Lie algebra \ mathfrak g of G is split into the sum \ mathfrak g = \ mathfrak h + \ mathfrak f of the Cartan subalgebra \ mathfrak h of H and its supplement \ mathfrak f so that There exists an open neighbourhood U of the unit of G such that any element g \ in U is uniquely brought into the form Let U_G be an open neighborhood of the unit of G such that U_G ^ 2 \ subset U , and let U_0 be an open neighborhood of the H-invariant center \ sigma_0 of the quotient G/H which consists of elements Then there is a local section s ( g \ sigma_0 ) = \ exp ( F ) of G \ to G/H over U_0 .
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Given options, please tell me the categories of all the listed entity words.Output format is "type1: word1; type2: word2". 
Option: location, person, organization 
Text: {0} 
 Entities:  
Answer:
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