Central Extensions of Restricted Affine Nilpotent Lie Algebras n₊(A⁽¹⁾₁)(p)

2022/08/07 by Tyler J. Evans, Evans, Tyler J., Alice Fialowski +1 · 2 citations
Mathematics · #17B50 #17B56 #17B67 #17B70 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2208.03783

openalex publication_date 2022/08/07 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Consider the maximal nilpotent subalgebra n₊(A₁⁽¹⁾) of the simplest affine algebra A₁⁽¹⁾ which is one of the ℕ-graded Lie algebras with minimal number of generators. We show truncated versions of this algebra in positive characteristic admit the structure of a family of restricted Lie algebras. We compute the ordinary and restricted 1- and 2-cohomology spaces with trivial coefficients by giving bases. With these we explicitly describe the restricted 1-dimensional central extensions.

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