Adjoint and Trivial Cohomologies of Nilpotent Complex Lie Algebras of Dimension

Table 12

Cohomology table for NLAs of dimension 5.

Algebra	Adjoint cocycles	Adjoint cohomology	Betti numbers
Rank 1
𝔤3×𝐶^3	(1,8,24,34,22,5)	(1,4,7,8,6,2)	(1,2,3,3,2,1)
Rank 2
𝐶^6‡■	(1,10,28,37,23,5)	(1,6,13,15,10,3)	(1,3,4,4,3,1)
𝔤5,6	(2,10,24,35,22,5)	(2,7,9,9,7,2)	(1,2,3,3,2,1)
𝔤5,3	(1,9,24,34,22,5)	(1,5,8,8,6,2)	(1,2,3,3,2,1)
Rank 3
𝔤5,4‡■	(1,15,30,41,24,5)	(1,11,20,21,15,4)	(1,4,5,5,4,1)
𝔤5,5	(2,13,31,39,23,5)	(2,10,19,20,12,3)	(1,3,6,6,3,1)
𝔤5,1	(2,11,28,37,23,5)	(2,8,14,15,10,3)	(1,3,4,4,3,1)
Rank 4
𝔤5,2	(3,16,37,43,24,5)	(3,14,28,30,17,4)	(1,4,7,7,4,1)
Rank 5
𝔤4×𝐶	(5,25,50,50,25,5)	(5,25,50,50,25,5)	(1,5,10,10,5,1)