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This article is cited in 3 scientific papers (total in 3 papers)
Cohomology of Restricted Filiform Lie Algebras ${\mathfrak m}_2^\lambda(p)$
Tyler J. Evansa, Alice Fialowskibc a Department of Mathematics, Humboldt State University, Arcata, CA 95521, USA
b Institute of Mathematics, University of Pécs, Pécs, Hungary
c Institute of Mathematics Eötvös Loránd University, Budapest, Hungary
Abstract:
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 $1<i<p$ and $[e_2,e_i]=e_{i+2}$ for $2<i<p-1$, 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.
Received: August 19, 2019; in final form November 24, 2019; Published online December 1, 2019
Citation:
Tyler J. Evans, Alice Fialowski, “Cohomology of Restricted Filiform Lie Algebras ${\mathfrak m}_2^\lambda(p)$”, SIGMA, 15 (2019), 095, 11 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1531 https://www.mathnet.ru/eng/sigma/v15/p95
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