Difference between revisions of "C7"

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|[[M(7,1,3)]] || <math>B_0(kPSL_2(13))</math> ||5 ||2 ||<math>C_2</math> || || ||1 ||1 || [[Image:M(7,1,3)tree.png|45px]]
 
|[[M(7,1,3)]] || <math>B_0(kPSL_2(13))</math> ||5 ||2 ||<math>C_2</math> || || ||1 ||1 || [[Image:M(7,1,3)tree.png|45px]]
 
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|[[M(7,1,4)]] || <math>k(C_7:C_3)</math> ||5 ||3 ||<math>C_3</math> || || ||1 ||1 || [[Image:M(7,1,4)tree.png|45px]]
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|[[M(7,1,4)]]
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|-
 
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|[[M(7,1,5)]] || <math>B_9(k(3.A_7))</math> ||5 ||3 ||<math>C_3</math> || || ||1 ||1 || [[Image:M(7,1,5)tree.png|45px]]
 
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|-
 
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|[[M(7,1,6)]] || <math>B_0(kA_7)</math> ||5 ||3 ||<math>C_3</math> || || ||1 ||1 || [[Image:M(7,1,6)tree.png|45px]]
 
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|-
 
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|[[M(7,1,7)]] || <math>B_{15}(k(6.A_7))</math> ||5 ||3 ||<math>C_3</math> |||| ||1 ||1 || [[Image:M(7,1,7)tree.png|45px]]
 
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|-
 
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|[[M(7,1,8)]] || <math>k(C_7:C_6)</math> ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,8)tree.png|45px]]
 
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|[[M(7,1,9)]] || <math>B_0(k(S_7))</math> ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,9)tree.png|45px]]
 
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|[[M(7,1,10)]] || <math>B_0(kPSL_3(29^3).3)</math> ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,10)tree.png|45px]]
 
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|[[M(7,1,11)]] || <math>B_{16}(k(2.J_2))</math> ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,11)tree.png|45px]]
 
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|[[M(7,1,12)]] || <math>B_{29}(k(2.Ru))</math> ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,12)tree.png|45px]]
 
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|[[M(7,1,13)]] || <math>B_0(k({}^2G_2(27)))</math> ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,13)tree.png|45px]]
 
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|-
 
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|[[M(7,1,14)]] || ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,14)tree.png|45px]]
 
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|-
 
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| || ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,15)tree.png|45px]]
 
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|-
 
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| || ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,16)tree.png|45px]]
 
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|-
 
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| || ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,17)tree.png|45px]]
 
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|-
 
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| || ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,18)tree.png|45px]]
 
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|-
 
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| || ||7 ||6 ||<math>C_6</math> |||| ||1 ||1 || [[Image:M(7,1,19)tree.png|45px]]
 
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|}
 
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To do:
 
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*The tree labelling the potential class M(7,1,14) is believed to be realised, but an example has not been confirmed.
 

Revision as of 17:02, 11 September 2018

Blocks with defect group [math]C_7[/math]

These are blocks with cyclic defect groups and so they are described by Brauer trees. There are candidate Brauer trees with no known block realising them.

All [math]k[/math]-Morita equivalence classes lift to [math]\mathcal{O}[/math]-classes. 

CLASSIFICATION INCOMPLETE
Class Representative [math]k(B)[/math] [math]l(B)[/math] Inertial quotients [math]{\rm Pic}_\mathcal{O}(B)[/math] [math]{\rm Pic}_k(B)[/math] [math]{\rm mf_\mathcal{O}(B)}[/math] [math]{\rm mf_k(B)}[/math] Notes
M(7,1,1) [math]kC_7[/math] 7 1 [math]1[/math] 1 1 M(7,1,1)tree.png
M(7,1,2) [math]kD_{15}[/math] 5 2 [math]C_2[/math] 1 1 M(7,1,2)tree.png
M(7,1,3) [math]B_0(kPSL_2(13))[/math] 5 2 [math]C_2[/math] 1 1 M(7,1,3)tree.png
M(7,1,4)
Retrieved from ‘http://wiki.manchester.ac.uk/blocks/index.php?title=C7&oldid=379’