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Cohomology of Restricted Filiform Lie Algebras ${\mathfrak m}_2^\lambda(p)$
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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For the $p$-dimensional filiform Lie algebra ${\mathfrak m}_2(p)$ over a field ${\mathbb F}$ of prime characteristic $p\ge 5$ with nonzero Lie brackets $[e_1,e_i] = e_{i+1}$ for $1$ and $[e_2,e_i]=e_{i+2}$ for $2$, we show that there is a family ${\mathfrak m}_2^{\lambda}(p)$ of restricted Lie algebra structures parameterized by elements $\lambda \in {\mathbb F}^p$. 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.
Keywords: restricted Lie algebra, central extension, cohomology, filiform Lie algebra. 
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     author = {Tyler J. Evans and Alice Fialowski},
     title = {Cohomology of {Restricted} {Filiform} {Lie} {Algebras} ${\mathfrak m}_2^\lambda(p)$},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2019},
     volume = {15},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a94/}
}
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Tyler J. Evans; Alice Fialowski. Cohomology of Restricted Filiform Lie Algebras ${\mathfrak m}_2^\lambda(p)$. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a94/

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