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1-cocycles of the Witt algebra with coefficients in tensor product of modules (2406.12565v1)
Published 18 Jun 2024 in math.RA, math-ph, math.MP, and math.RT
Abstract: In this paper, we classify 1-cocycles of the Witt algebra with coefficients in the tensor product of two arbitrary tensor density modules. In a special case, we recover a theorem originally established by Ng and Taft in \cite{NT}. Furthermore, by these 1-cocycles, we determine Lie bialgebra structures over certain infinite-dimensional Lie algebras containing the Witt algebra.