Cohomology of Restricted Filiform Lie Algebras m₂^λ(p) · arXivDesk
1901.07532Jan 20, 2019We use the restricted cochain complex and differentials in arXiv:1801.08178 to complete the analogous calculations for the restricted algebras $\mathfrak{m}_2^λ(p)$
Cohomology of Restricted Filiform Lie Algebras m2λ(p)
For the p-dimensional filiform Lie algebra m2(p) over a field F of prime characteristic p≥5
Nearby in the stack
with nonzero Lie brackets
[e1,ei]=ei+1
for
1<i<p
and
[e2,ei]=ei+2
for
2<i<p−1
, we show that there is a family
m2λ(p)
of restricted Lie algebra structures parameterized by elements
λ∈Fp
. We explicitly describe bases for the ordinary and restricted 1- and 2-cohomology spaces with trivial coefficients, and give formulas for the bracket and
[p]
-operations in the corresponding restricted one-dimensional central extensions.