2018/05/22 by Jill Ecker, Martin Schlichenmaier · 5 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Cohomology #Group cohomology #Homotopy and Cohomology in Algebraic Topology #Sketch #Virasoro algebra #Witt algebra #hep-th #math-ph #math.MP #math.QA #math.RA #msc:14D15 #msc:17B56 #msc:17B65 #msc:17B66 #msc:17B68 #msc:81R10 #msc:81T40
paper · pdf · doi:10.1088/1742-6596/1194/1/012032
published in Journal of Physics Conference Series 1194, 012032 (IOP Publishing) · 21 pages
arxiv created 2018/05/22 · openalex created_date 2018/06/01 · openalex publication_date 2019/04/01 · arxiv updated 2019/05/22 · openalex updated_date 2026/08/05
In this contribution, we provide the results on the low-dimensional algebraic cohomology with values in the trivial and the adjoint module of the Witt and the Virasoro algebra over a field with . A sketch of the various proofs is given, the details can be found in previous articles of the authors. More precisely, we give a summary of results known concerning the zeroth, first and second algebraic cohomology of the Witt and the Virasoro algebra, and we present some details about the more recent results related to the third algebraic cohomology. It has to be noted that we are dealing entirely with algebraic cohomology, meaning that our results are valid for any concrete realization of the Witt and the Virasoro algebra. Moreover, our results are independent of any underlying topology chosen.