Adjoint and Trivial Cohomologies of Nilpotent Complex Lie Algebras of Dimension

Table 13

Cohomology table for NLAs of dimension 𝔤₃×𝐶𝟚

Algebra	Adjoint cocycles	Adjoint cohomology	Betti numbers
𝐶^5‡■	(1,7,15,14,4)	(1,4,6,5,2)	(1,2,2,2,1)
≤4.	(2,10,19,15,4)	(2,8,13,10,3)	(1,3,4,3,1)
𝔤4(dim4,rk2)	(4,16,24,16,4)	(4,16,24,16,4)	(1,4,6,4,1)
𝔤3×𝐶(dim4,rk3)	(1,6,8,3)	(1,4,5,2)	(1,2,2,1)
𝐶^4(abel.)‡■(dim4,rk4)	(3,9,9,3)	(3,9,9,3)	(1,3,3,1)
𝔤3(dim3,rk2)	(2,4,2)	(2,4,2)	(1,2,1)
𝐶^3(abel.)‡■(dim3,rk3)	(1,1)	(1,1)	(1,1)