1-cocycles of the Witt algebra with coefficients in tensor product of modules

2024/06/18 by Shoulan Gao, Dong Liu, Gao, Shoulan +3
Mathematics · #17B05 #17B62 #17B65 #17B68 #Advanced Topics in Algebra #Algebra over a field #Algebra representation #Algebraic structures and combinatorial models #Cellular algebra #Commutative Algebra and Its Applications #FOS: Mathematics #FOS: Physical sciences #Geometry #Mathematical Physics (math-ph) #Mathematics #Product (mathematics) #Pure mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Tensor (intrinsic definition) #Tensor contraction #Tensor product #Tensor product of Hilbert spaces #Tensor product of modules #Witt algebra

paper · pdf · doi:10.48550/arxiv.2406.12565

openalex publication_date 2024/06/18 · openalex created_date 2024/06/20 · openalex updated_date 2026/07/28

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 \citeNT. Furthermore, by these 1-cocycles, we determine Lie bialgebra structures over certain infinite-dimensional Lie algebras containing the Witt algebra.

Related

• Length two extensions of modules for the Witt Algebra
• Tensor products of the defining representations over the Witt algebra in positive characteristic
• Determination of the 2- cocycles for the three point Witt algebra
• Tensor modules over Witt superalgebras
• Simple weight modules with finite-dimensional weight spaces over Witt superalgebras