Adjoint and Trivial Cohomologies of Nilpotent Complex Lie Algebras of Dimension

Table 3

Cohomology table for NLAs of dimension 7: rank 0.

Algebra	Adjoint cocycles	Adjoint cohomology	Betti numbers
(𝔤6,11×ℂ,𝔤4×𝔤3)	(1,10,48,114,147,109,44,7)	(1,4,9,15,16,11,6,2)	(1,2,3,4,4,3,2,1)
(2,12,31,48,51,38,18,4)	(1,10,49,113,147,109,44,7)	(1,4,10,15,15,11,6,2)	(1,2,3,4,4,3,2,1)
𝔤7,0.1	(1,11,50,116,149,110,44,7)	(1,5,12,19,20,14,7,2)	(1,2,4,6,6,4,2,1)
𝔤7,0.2	(1,10,48,114,147,110,44,7)	(1,4,9,15,16,12,7,2)	(1,2,3,4,4,3,2,1)
𝔤7,0.3	(1,10,48,114,147,110,44,7)	(1,4,9,15,16,12,7,2)	(1,2,3,4,4,3,2,1)
𝔤7,0.4(𝜆)	(1,10,48,114,148,110,44,7)	(1,4,9,15,17,13,7,2)	(1,2,3,5,5,3,2,1)
𝔤7,0.5	(1,10,49,115,148,110,44,7)	(1,4,10,17,18,13,7,2)	(1,2,3,4,4,3,2,1)
𝔤7,0.6	(1,10,50,114,148,112,45,7)	(1,4,11,17,17,15,10,3)	(1,3,4,4,4,4,3,1)