Coxeter group

English Etymology Named for British-born Canadian mathematician Harold Scott MacDonald Coxeter H. S. M. Coxeter (1907–2003). Noun en mathematics geometry group theory Any of a class of groups whose finite cases are precisely the finite reflection groups (including the symmetry groups of polytopes), but which are more varied in their infinite cases, and whose range of application encompasses various areas of mathematics. en 1993 B. Mühlherr Coxeter groups in Coxeter groups Albrecht Beutelspacher; F. de Clerck Finite Geometries and Combinatorics https://books.google.com.au/books?id=5Uau9KpdZ58C&pg=PA277&dq=%22Coxeter+group%22%7C%22Coxeter+groups%22&hl=en&sa=X&ved=0ahUKEwjB0476xvnMAhXIJJQKHdlnAboQ6AEIugIwSA#v=onepage&q=%22Coxeter%20group%22%7C%22Coxeter%20groups%22&f=false 277 We may ask in general which Coxeter groups arise as subgroups of a given Coxeter group. This question is of course far too general. However, there are Coxeter groups which arise canonically as subgroups of a given Coxeter group. en 2007 Michael B. Smythe; Julian Webster 12: Discrete Spatial Models Marco Aiello; Ian Pratt-Hartmann; Johan van Benthem Handbook of Spatial Logics https://books.google.com.au/books?id=w6_T3KqZnrYC&pg=PA795&dq=%22Coxeter+group%22%7C%22Coxeter+groups%22&hl=en&sa=X&ved=0ahUKEwi1xbegyvnMAhUC4qYKHa4kAoY4ZBDoAQiDBDBV#v=onepage&q=%22Coxeter%20group%22%7C%22Coxeter%20groups%22&f=false 795 The above definitions, of Cayley graph, reflection, wall, half-space, folding, Bruhat order, etc., work for any Coxeter group. en 2012 Daniel Allcock The Reflective Lorentzian Lattices of Rank 3 Memoirs of the American Mathematical Society 1033 https://books.google.com.au/books?id=tZMCAQAAQBAJ&pg=PR7&dq=%22Coxeter+group%22%7C%22Coxeter+groups%22&hl=en&sa=X&ved=0ahUKEwi1xbegyvnMAhUC4qYKHa4kAoY4ZBDoAQiPATAV#v=onepage&q=%22Coxeter%20group%22%7C%22Coxeter%20groups%22&f=false vii The problem of classifying all reflective lattices of given rank is also of interest in its own right from the perspectives of Coxeter groups and arithmetic subgroups of O(n,1). Related terms en Coxeter-Dynkin diagram en Coxeter element en Coxeter matrix en Coxeter number en Coxeter system en eponyms