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Numerical classification of unimodular Einstein Lie groups towards resolving the long-standing generalized Alekseevskii conjecture

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alekseevskii

Numerical classification of unimodular Einstein Lie groups towards resolving the long-standing generalized Alekseevskii conjecture

Updated in 2020 for modern Python/OpenCL

Notes

  • In the 1970s, it was conjectured by D. Alekseevskii that any (non-compact) homogeneous Einstein space of negative scalar curvature is diffeomorphic to R^n. In other words, the Classical Alekseevskii Conjecture states: Given a homogeneous Einstein space G/K with negative scalar curvature, K must be a maximal compact subgroup of G [Jablonski].
  • blocking contains an implementation of a numerical search algorithm in python and cython
  • tests include a simple benchmark of computing spatial array index
  • opencl_helper.py provides a nice wrapper around pyopencl for loading simple kernels and running sequences over sets of numpy arrays

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Numerical classification of unimodular Einstein Lie groups towards resolving the long-standing generalized Alekseevskii conjecture

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