Proposition 7.6, the characteristic-two decomposition, for a representation-finite algebra #
prop:hochschild-mesh-restriction (weights-and-parameters.tex): "In characteristic two,
there is a subset I₀ ⊆ I such that HH²(A₀)_{>0} = ⊕_{i ∈ I₀} HH²(A₀)_{χ_i},
dim_k HH²(A₀)_{χ_i} = 1." Here HH²(A₀)_{>0} is computed by normalized relative cocycles
modulo coboundaries in each internal degree q > 0 (exists_rel_cobdry), the characters are
taken in L = W(P) through the universal mesh weight (Lemma 7.4), and the rows are those of
Proposition 6.1. The injection Ψ of the first part is fullHochschildComparison_ar.
The vertex idempotents of A₀ have mesh weight zero.
Proposition 7.6, characteristic two (prop:hochschild-mesh-restriction), for A₀ of a
basic connected representation-finite algebra: with the rows p_i of Proposition 6.1
and the characters χ_i = w(p_i) − ν_{v_i} in L = W(P) (pairwise distinct), there are
I₀ = {R₀, …, R_{n−1}} ⊆ I and normalized relative cocycles μ_i of character χ_{R_i} and
positive degree, not coboundaries, such that HH²(A₀)_{χ_R} = 0 for rows outside I₀, the
classes of the μ_i span HH²(A₀)_{>0} in every internal degree, are independent (the sum is
direct), and every class of character χ_{R_i} is a multiple of [μ_i]
(dim HH²(A₀)_{χ_i} = 1).