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Blocks with basic algebras of dimension at most 12

In [Li18] Markus Linckelmann calculated the [math]k[/math]-algebras of dimension at most twelve which occur as basic algebras of blocks of finite groups, with the exception of one case of dimension 9.

Dimension	Class	Defect group	Representative	[math]\dim_k(Z(A))[/math]	[math]l(A)[/math]	Notes
1	M(1,1,1)	[math]1[/math]	[math]k1[/math]	1	1	Blocks of defect zero
2	M(2,1,1)	[math]C_2[/math]	[math]kC_2[/math]	2	1
3	M(3,1,1)	[math]C_3[/math]	[math]kC_3[/math]	3	1
4	M(4,1,1)	[math]C_4[/math]	[math]kC_4[/math]	4	1
4	M(4,2,1)	[math]C_2 \times C_2[/math]	[math]k(C_2 \times C_2)[/math]	4	1
5	M(5,1,1)	[math]C_5[/math]	[math]kC_5[/math]	5	1
6	M(3,1,2)	[math]C_3[/math]	[math]kS_3[/math]	3	2
7	M(5,1,3)	[math]C_5[/math]	[math]B_0(kA_5)[/math]	4	2
7	M(7,1,1)	[math]C_7[/math]	[math]kC_7[/math]	7	1
8	M(8,1,1)	[math]C_8[/math]	[math]kC_8[/math]	8	1
8	M(8,2,1)	[math]C_4 \times C_2[/math]	[math]k(C_4 \times C_2)[/math]	8	1
8	M(8,3,1)	[math]D_8[/math]	[math]kD_8[/math]	5	1
8	M(8,4,1)	[math]Q_8[/math]	[math]kQ_8[/math]	5	1
8	M(8,5,1)	[math]C_2 \times C_2 \times C_2[/math]	[math]k(C_2 \times C_2 \times C_2)[/math]	8	1
8	M(7,1,3)	[math]C_7[/math]	[math]B_0(kPSL_2(13))[/math]	5	2
9	M(9,1,1)	[math]C_9[/math]	[math]kC_9[/math]	9	1
9	M(9,1,3)	[math]C_9[/math]	[math]B_0(kSL_2(8))[/math]	6	2
9	M(9,2,1)	[math]C_3 \times C_3[/math]	[math]k(C_3 \times C_3)[/math]	9	1
9	M(9,2,2)	[math]C_3 \times C_3[/math]	Faithful block of [math]k((C_3 \times C_3):D_8)[/math], in which [math]Z(D_8)[/math] acts trivially	6	1
9		[math]C_3 \times C_3[/math]	?	6	2	Unknown
10	M(5,1,2)	[math]C_5[/math]	[math]kD_{10}[/math]	4	2
10	M(11,1,3)	[math]C_{11}[/math]	[math]B_0(kSL_2(32))[/math]	7	2
11	M(8,3,3)	[math]D_8[/math]	[math]kS_4[/math]	5	2
11	M(7,1,6)	[math]C_7[/math]	[math]B_0(kA_7)[/math]	5	3
11	M(11,1,1)	[math]C_{11}[/math]	[math]kC_{11}[/math]	11	1
11	M(13,1,3)	[math]C_{13}[/math]	[math]B_0(kPSL_2(25))[/math]	8	2
12	M(4,2,3)	[math]C_2 \times C_2[/math]	[math]kA_4[/math]	4	3