International Journal of Mathematics and Mathematical Sciences

Research Article

Adjoint and Trivial Cohomologies of Nilpotent Complex Lie Algebras of Dimension

Table 11

Cohomology table for NLAs of dimension 6.


Algebra	Adjoint cocycles	Adjoint cohomology	Betti numbers

Rank 1

	(1,11,40,71,68,33,6)	(1,6,15,21,19,11,3)	(1,3,5,6,5,3,1)
	(1,10,36,67,64,32,6)	(1,5,10,13,11,6,2)	(1,2,3,4,3,2,1)
	(1,9,35,66,64,32,6)	(1,4,8,11,10,6,2)	(1,2,3,4,3,2,1)
	(1,8,34,64,63,32,6)	(1,3,6,8,7,5,2)	(1,2,2,2,2,2,1)

Rank 2

	(2,12,42,72,68,33,6)	(2,8,18,24,20,11,3)	(1,3,5,6,5,3,1)
	(2,14,44,75,69,33,6)	(2,10,22,29,24,12,3)	(1,3,6,8,6,3,1)
	(2,13,42,72,68,33,6)	(2,9,19,24,20,11,3)	(1,3,5,6,5,3,1)
	(1,12,41,72,68,33,6)	(1,7,17,23,20,11,3)	(1,3,5,6,5,3,1)
	(1,12,40,71,68,33,6)	(1,7,16,21,19,11,3)	(1,3,5,6,5,3,1)
	(1,10,38,68,67,33,6)	(1,5,12,16,15,10,3)	(1,3,4,4,4,3,1)
	(2,11,37,68,66,32,6)	(2,7,12,15,14,8,2)	(1,2,4,6,4,2,1)
	(1,10,36,67,66,32,6)	(1,5,10,13,13,8,2)	(1,2,4,6,4,2,1)
	(1,11,37,67,64,32,6)	(1,6,12,14,11,6,2)	(1,2,3,4,3,2,1)
	(1,9,34,64,63,32,6)	(1,4,7,8,7,5,2)	(1,2,2,2,2,2,1)
	(2,12,40,71,68,33,6)	(2,8,16,21,19,11,3)	(1,3,5,6,5,3,1)

Rank 3

	(2,17,50,82,74,34,6)	(2,13,31,42,36,18,4)	(1,4,8,10,8,4,1)
	(1,14,44,73,72,34,6)	(1,9,22,27,25,16,4)	(1,4,6,6,6,4,1)
	(3,18,48,78,72,33,6)	(3,15,30,36,30,15,3)	(1,3,8,12,8,3,1)
	(2,13,43,74,69,33,6)	(2,9,20,27,23,12,3)	(1,3,6,8,6,3,1)
	(2,15,45,75,69,33,6)	(2,11,24,30,24,12,3)	(1,3,6,8,6,3,1)
	(1,11,41,70,68,33,6)	(1,6,16,21,18,11,3)	(1,3,5,6,5,3,1)
	(2,15,47,79,76,34,6)	(2,11,26,36,32,17,4)	(1,4,7,8,7,4,1)
	(3,15,42,72,69,33,6)	(3,12,21,24,21,12,3)	(1,3,5,6,5,3,1)
	(2,13,41,71,68,33,6)	(2,9,18,22,19,11,3)	(1,3,5,6,5,3,1)

Rank 4

	(2,21,55,86,79,35,6)	(2,17,40,51,45,24,5)	(1,5,9,10,9,5,1)
	(3,19,55,86,75,34,6)	(3,16,38,51,41,19,4)	(1,4,9,12,9,4,1)
	(3,17,48,79,73,34,6)	(3,14,29,37,32,17,4)	(1,4,7,8,7,4,1)
	(2,16,50,82,74,34,6)	(2,12,30,42,36,18,4)	(1,4,8,10,8,4,1)

Rank 5

	(4,24,65,97,81,35,6)	(4,22,53,72,58,26,5)	(1,5,11,14,11,5,1)

Rank 6 (abelian)

	(6,36,90,120,90,36,6)	(6,36,90,120,90,36,6)	(1,6,15,20,15,6,1)