{'fraction_non_alphanumeric': 0.029288702928870293, 'fraction_numerical': 0.00697350069735007, 'mean_word_length': 4.933884297520661, '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}}
A New Construction of 2-Dimensional Particles Algebra and Non-Commutative Geometry

The fundamental algebra of non-commutative geometry and the annihilation and creation operators are redefined by considering the statistical properties of d-dimensional space (d ≥ 2). Thus, a new construction of 2-dimensional particles algebra is given. As a remark, the obtained algebra is a deformed Heisenberg algebra and could be treated as a unified particles algebra. To prove it, the cases of d and the statistical parameter ν are discussed. By considering ν ∈ [0, 1], the algebra is realized as a deformed version of Heisenberg algebra extended by a polynomial in some operator and deformed in terms of statistical parameter.