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Gröbner–Shirshov bases for non‐crystallographic Coxeter groups
Author(s) -
Lee Jeong-Yup,
Lee Dong-il
Publication year - 2019
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s2053273319002092
Subject(s) - coxeter group , mathematics , combinatorics , group (periodic table) , monomial , basis (linear algebra) , longest element of a coxeter group , homogeneous space , type (biology) , pure mathematics , algebra over a field , coxeter complex , artin group , physics , geometry , biology , ecology , quantum mechanics
For the group algebra of the finite non‐crystallographic Coxeter group of type H 4 , its Gröbner–Shirshov basis is constructed as well as the corresponding standard monomials, which describe explicitly all symmetries acting on the 120‐cell and produce a natural operation table between the 14400 elements for the group.