Some Algebraic Properties of the Wilson Loop

Table 1

An example of a noncommutative and nonassociative Wilson loop of order 12.

c	0	1	2	3	4	5	6	7	8	9	10	11
0	0	1	2	3	4	5	6	7	8	9	10	11
1	1	2	0	4	5	3	7	8	6	10	11	9
2	2	0	1	5	3	4	8	6	7	11	9	10
3	3	4	5	0	1	2	10	11	9	8	6	7
4	4	5	3	1	2	0	11	9	10	6	7	8
5	5	3	4	2	0	1	9	10	11	7	8	6
6	6	7	8	11	9	10	0	1	2	4	5	3
7	7	8	6	9	10	11	1	2	0	5	3	4
8	8	6	7	10	11	9	2	0	1	3	4	5
9	9	10	11	7	8	6	5	3	4	0	1	2
10	10	11	9	8	6	7	3	4	5	1	2	0
11	11	9	10	6	7	8	4	5	3	2	0	1