Length two extensions of modules for the Witt Algebra

2015/10/23 by Kathlyn Dykes, Dykes, Kathlyn
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1510.06792

27 pages, 3 figures

arxiv created 2015/10/23 · openalex publication_date 2015/10/23 · arxiv updated 2015/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish an explicit classification of length two extensions of tensor modules for the Witt algebra using the cohomology of the Witt algebra with coefficients in the module of the space of homomorphisms between the two modules of interest. To do this we extended our module to a module that has a compatible action of the commutative algebra of Laurent polynomials in one variable. In this setting, we are be able to directly compute all possible 1-cocycles.

Related

• 1-cocycles of the Witt algebra with coefficients in tensor product of modules
• Extensions of simple modules for the Witt algebra
• Representations of loop extended Witt algebras
• Tensor products of the defining representations over the Witt algebra in positive characteristic
• The generalized Witt algebras using additive maps