Adjoint and Trivial Cohomologies of Nilpotent Complex Lie Algebras of Dimension

Table 7

Cohomology table for NLAs of dimension 7: rank 4.

Algebra	Adjoint cocycles	Adjoint cohomology	Betti numbers
𝔤6,18×ℂ	(3,20,71,149,174,122,46,7)	(3,16,42,73,78,51,21,4)	(1,4,11,16,16,11,4,1)
𝔤5,6×ℂ^2	(3,25,78,157,178,123,46,7)	(3,21,54,88,90,56,22,4)	(1,4,12,18,18,12,4,1)
𝔤7,4.1	(2,21,72,150,175,125,47,7)	(2,16,44,75,80,55,25,5)	(1,5,10,16,16,10,5,1)
𝔤7,4.2	(1,28,91,140,189,134,48,7)	(1,22,70,84,84,78,35,6)	(1,6,14,14,14,14,6,1)
𝔤7,4.3	(3,24,81,157,184,127,47,7)	(3,20,56,91,96,66,27,5)	(1,5,12,18,18,12,5,1)
𝔤7,4.4	(2,20,70,138,171,125,47,7)	(2,15,41,61,64,51,25,5)	(1,5,10,12,12,10,5,1)
𝔤6,1×ℂ	(4,25,80,153,178,123,46,7)	(4,22,56,86,86,56,22,4)	(1,4,11,20,20,11,4,1)
𝔤6,2×ℂ	(3,19,68,140,169,120,46,7)	(3,15,38,61,64,44,19,4)	(1,4,9,14,14,9,4,1)
𝔤6,3×ℂ‡■	(3,21,72,143,170,120,46,7)	(3,17,44,68,68,45,19,4)	(1,4,9,14,14,9,4,1)
𝔤6,4×ℂ	(2,16,63,132,163,119,46,7)	(2,11,30,48,50,37,18,4)	(1,4,8,11,11,8,4,1)
𝔤6,6×ℂ	(3,22,75,149,179,126,47,7)	(3,18,48,77,83,60,26,5)	(1,5,11,15,15,11,5,1)
𝔤6,9×ℂ	(4,22,68,135,166,120,46,7)	(4,19,41,56,56,41,19,4)	(1,4,8,11,11,8,4,1)
𝔤5,3×ℂ^2	(3,19,65,133,164,119,46,7)	(3,15,35,51,52,38,18,4)	(1,4,8,11,11,8,4,1)
𝔤5,4×ℂ^2‡■	(2,17,63,132,164,119,46,7)	(2,12,31,48,51,38,18,4)	(1,4,8,11,11,8,4,1)