Comparison
R = Zp
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R = kQ, Q a Dynkin quiver.
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Hall algebra H(Zp) = "algebra of partitions"
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Hall algebra H(kQ)
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A partition is of the form
(1a(1),2a(2),...,ta(t),...)
| with a map a : N1 → N0 with finite support.
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Index set:
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the set
{ maps N1 → N0 with finite support}
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the set
{ maps Φ+ → N0 }
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Parts:
| elements in N1
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Φ+ the positive roots.
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| H(R) is commutative
| The commutators are of interest!
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| Hall polynomialsBasic Hall polynomials (M, N, N' indec.)
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degree at most 5
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