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𝔤 -quasi-Frobenius Lie algebras

David N. Pham (2016)

Archivum Mathematicum

A Lie version of Turaev’s G ¯ -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a 𝔤 -quasi-Frobenius Lie algebra for 𝔤 a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra ( 𝔮 , β ) together with a left 𝔤 -module structure which acts on 𝔮 via derivations and for which β is 𝔤 -invariant. Geometrically, 𝔤 -quasi-Frobenius Lie algebras are the Lie algebra structures associated to symplectic...

(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras

Chao Wang, Xiao Yan Yang (2017)

Czechoslovak Mathematical Journal

Let Λ = A M 0 B be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective Λ -modules under the condition that M is a cocompatible ( A , B ) -bimodule, we establish a recollement of the stable category Ginj ( Λ ) ¯ . We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over Λ .

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