In mathematics, an Artin group (or generalized braid group) is a group with a presentation of the form
where
- .
For, denotes an alternating product of and of length, beginning with . For example,
and
- .
If, then there is (by convention) no relation for and .
The integers can be organized into a symmetric matrix, known as the Coxeter matrix of the group. Each Artin group has as a quotient the Coxeter group with the same set of generators and Coxeter matrix. The kernel of the homomorphism to the associated Coxeter group, known as the pure Artin group, is generated by relations of the form .
Read more about Artin Group: Classes of Artin Groups
Famous quotes containing the word group:
“Instead of seeing society as a collection of clearly defined “interest groups,” society must be reconceptualized as a complex network of groups of interacting individuals whose membership and communication patterns are seldom confined to one such group alone.”
—Diana Crane (b. 1933)