{'fraction_non_alphanumeric': 0.038910505836575876, 'fraction_numerical': 0.005836575875486381, 'mean_word_length': 4.202020202020202, '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}}
Automorphisms of Endomorphism Monoids of 1-Simple Free Algebras

For any set X and any variety 𝒱 of algebras, let 𝒜 = 𝒜 𝒱(X) be the free algebra in 𝒱 with set X of free generators, and let End(𝒜) be the monoid of endomorphisms of 𝒜. We provide a general approach to the description of the automorphism group of End(𝒜), and some subsemigroups of End(𝒜), provided that 𝒜 is 1-simple. We show that every automorphism of End(𝒜) is a unique extension of an automorphism of the monoid of endomorphisms of rank at most 1.