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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(kPSL_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 [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(kPSL_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