Bounding and unbounding higher extensions for SL2
We analyse the recursive formula found for various Ext groups for SL2(k), k a field of characteristic p , and derive various generating functions for these groups. We use this to show that the growth rate for the cohomology of SL2(k) is at least exponential. In particular, max{dimExtSL2(k)i (k,Δ(a))...
| Príomhchruthaitheoirí: | , , |
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| Formáid: | Journal article |
| Teanga: | English |
| Foilsithe / Cruthaithe: |
2013
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| Achoimre: | We analyse the recursive formula found for various Ext groups for SL2(k), k a field of characteristic p , and derive various generating functions for these groups. We use this to show that the growth rate for the cohomology of SL2(k) is at least exponential. In particular, max{dimExtSL2(k)i (k,Δ(a))|a,i∈N} has (at least) exponential growth for all p We also show that max{dimExtSL2(k)i(k,Δ(a))|a∈N} for a fixed i is bounded. © 2013 Elsevier Inc. |
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