{'fraction_non_alphanumeric': 0.03880597014925373, 'fraction_numerical': 0.0, 'mean_word_length': 3.8, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Krull dimension of factor rings of the enveloping algebra of a semi-simple Lie algebra

Let g be a semi-simple complex Lie algebra with enveloping algebra U(g). It is shown that the Krull dimension of U(g) is bounded above by dim g − r, where r is half the minimal dimension of a non-trivial G orbit in g (G is the adjoint group of g).