Coxeter diagram

English Noun en geometry algebra A Coxeter-Dynkin diagram. en 1991 Gregori A. Margulis Discrete Subgroups of Semisimple Lie Groups 358 https://books.google.com.au/books?id=V9z2cjHOhVoC&pg=PA358&dq=%22Coxeter+diagram%22%7C%22Coxeter+diagrams%22&hl=en&sa=X&ved=0ahUKEwjhice-pa_NAhXCi5QKHaq0DvsQ6AEIbzAN#v=onepage&q=%22Coxeter%20diagram%22%7C%22Coxeter%20diagrams%22&f=false It suffices to make use of the tables above and observe that the Coxeter diagram of a direct sum of C-matrices is the disconnected union of the Coxeter diagrams of the summands.For the description of C−-matrices satisfying condition (2) we shall use Coxeter diagrams with the additional stipulation that in case aij < −1 the vertices vi and vj are joined by a dotted line with index −aij. By the Coxeter diagram of a Coxeter polyhedron and a lattice generated by reflections we mean the Coxeter diagram of the corresponding C−-matrix. en 1993 B. Mühlherr Coxeter groups in Coxeter groups Albrecht Beutelspacher; F. Buekenhout; J. Doyen; F. de Clerck; J. A. Thas; J. W. P. Hirschfeld Finite Geometries and Combinatorics 2nd International Conference https://books.google.com.au/books?id=5Uau9KpdZ58C&pg=PA277&dq=%22Coxeter+diagram%22%7C%22Coxeter+diagrams%22&hl=en&sa=X&ved=0ahUKEwjhice-pa_NAhXCi5QKHaq0DvsQ6AEIsQEwGQ#v=onepage&q=%22Coxeter%20diagram%22%7C%22Coxeter%20diagrams%22&f=false 277 An automorphism of a Coxeter diagram M leads in a natural way to a Coxeter subgroup of the Coxeter group of type M. We introduce admissible partitions of Coxeter diagrams in order to generalize this situation. en 2008 Peter Abramenko; Kenneth S. Brown Buildings: Theory and Applications https://books.google.com.au/books?id=7AJf5J55h28C&pg=PA259&dq=%22Coxeter+diagram%22%7C%22Coxeter+diagrams%22&hl=en&sa=X&ved=0ahUKEwjhice-pa_NAhXCi5QKHaq0DvsQ6AEIWjAK#v=onepage&q=%22Coxeter%20diagram%22%7C%22Coxeter%20diagrams%22&f=false 259 The Coxeter diagrams of type E7 and E8 have no nontrivial automorphisms, so σ0 is trivial in those cases.The Coxeter diagram of type F4 has a unique nontrivial automorphism, but σ0 is trivial in this case. One can see this by using the Dynkin diagram instead of the Coxeter diagram and noting that it does not have any nontrivial automorphisms. en eponyms