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Malcev-Moduln.

Renate Carlsson (1976)

Journal für die reine und angewandte Mathematik

Mappings on some reflexive algebras characterized by action on zero products or Jordan zero products

Yunhe Chen, Jiankui Li (2011)

Studia Mathematica

Let 𝓛 be a subspace lattice on a Banach space X and let δ: Alg𝓛 → B(X) be a linear mapping. If ⋁ {L ∈ 𝓛 : L₋ ⊉ L}= X or ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0), we show that the following three conditions are equivalent: (1) δ(AB) = δ(A)B + Aδ(B) whenever AB = 0; (2) δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) whenever AB + BA = 0; (3) δ is a generalized derivation and δ(I) ∈ (Alg𝓛)'. If ⋁ {L ∈ 𝓛 : L₋ ⊉ L} = X or ⋁ {L₋ : L ∈ 𝓛, L₋ ⊉ L} = (0) and δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A)...

Maximal solvable extensions of filiform algebras

Libor Šnobl (2011)

Archivum Mathematicum

It is already known that any filiform Lie algebra which possesses a codimension 2 solvable extension is naturally graded. Here we present an alternative derivation of this result.

Miura opers and critical points of master functions

Evgeny Mukhin, Alexander Varchenko (2005)

Open Mathematics

Critical points of a master function associated to a simple Lie algebra 𝔤 come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra t 𝔤 . The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms...

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