Classification of Ordered Type Soliton Metric Lie Algebras by a Computational Approach

Table 6

The 9-dimensional candidates of nullities 6 and 8.

	Lie bracket	Index	Nullity
1	(0, 0, 1.12, 1.13, 1.14 + 1.23, 0, 1.16 + 1.25 + 1.34, 1.17 + 1.26 + 1.35, 1.18 + 1.27 + 1.36 + 1.45)	6	6
2	(0, 0, 1.12, 1.13, 1.14, 1.15, 1.16 + 1.25 + 1.34, 1.17 + 1.26 + 1.35, 1.18 + 1.27 + 1.36 + 1.45)	7	6
3	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.34, 1.17 + 1.35, 1.18 + 1.27 + 1.36 + 1.45)	7	6
4	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.34, 1.17 + 1.26 + 1.35, 1.18 + 1.36 + 1.45)	7	6
5	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.34, 1.17 + 1.26, 1.18 + 1.27 + 1.36 + 1.45)	7	6
6	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.34, 1.17 + 1.26 + 1.35, 1.18 + 1.27 + 1.45)	7	6
7	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.34, 1.17 + 1.26 + 1.35, 1.18 + 1.27 + 1.36)	7	6
8	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.35, 1.18 + 1.36 + 1.45)	7	6
9	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25, 1.17 + 1.35, 1.18 + 1.27 + 1.36 + 1.45)	7	6
10	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17, 1.18 + 1.27 + 1.36 + 1.45)	7	6
11	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.35, 1.18 + 1.27 + 1.45)	7	6
12	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.35, 1.18 + 1.27 + 1.36)	7	6
13	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25, 1.17 + 1.26 + 1.35, 1.18 + 1.36 + 1.45)	7	6
14	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.26, 1.18 + 1.36 + 1.45)	7	6
15	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.26 + 1.35, 1.18 + 1.45)	7	6
16	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.26 + 1.35, 1.18 + 1.36)	7	6
17	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25, 1.17 + 1.26, 1.18 + 1.27 + 1.36 + 1.45)	7	6
18	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25, 1.17 + 1.26 + 1.35, 1.18 + 1.27 + 1.45)	7	6
19	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25, 1.17 + 1.26 + 1.35, 1.18 + 1.27 + 1.36)	7	6
20	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.26, 1.18 + 1.27 + 1.45)	7	6
21	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.26, 1.18 + 1.27 + 1.36)	7	6
22	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.26 + 1.35, 1.18 + 1.27)	7	6
23	(0, 0, 1.12, 1.13, 1.14 + 1.23, 1.15 + 1.24, 1.16 + 1.25 + 1.34, 1.17 + 1.26 + 1.35, 1.18 + 1.27 + 1.36 + 1.45)	7	8