What question did this study set out to answer?

The research aims to explore Lie bialgebra structures within not-finitely graded Lie algebras of block type.

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March 29, 2026Open Access

Lie Bialgebra Structures on Not-Finitely Graded Lie Algebras B(Γ) of Block Type

Key Points

The research aims to explore Lie bialgebra structures within not-finitely graded Lie algebras of block type.
Investigation of Lie bialgebra structures on B(Γ) algebras.
Proof of the triviality of the first cohomology group H1(B(Γ), B(Γ) ⊗ B(Γ)) = 0.
All Lie bialgebra structures on B(Γ) are shown to be triangular coboundary.

Abstract

In this paper, Lie bialgebra structures on a class of not-finitely graded Lie algebras B() of Block type are investigated.By proving the triviality of the first cohomology group of B() with coefficients in its adjoint tensor module, namely, H 1 (B(), B() B()) = 0 , we obtain that all Lie bialgebra structures on B() are triangular coboundary.

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