Generalized Coxeter Groups¶
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sage.categories.generalized_coxeter_groups.
GeneralizedCoxeterGroups
¶ The category of generalized Coxeter groups.
A generalized Coxeter group is a group with a presentation of the following form:
\[\langle s_i \mid s_i^{p_i}, s_i s_j \cdots = s_j s_i \cdots \rangle,\]where \(p_i > 1\), \(i \in I\), and the factors in the braid relation occur \(m_{ij} = m_{ji}\) times for all \(i \neq j \in I\).
EXAMPLES:
sage: from sage.categories.generalized_coxeter_groups import GeneralizedCoxeterGroups sage: C = GeneralizedCoxeterGroups(); C Category of generalized coxeter groups