Reference : The Vanishing of Low-Dimensional Cohomology Groups of the Witt and the Virasoro algebra

	Document type :	E-prints/Working papers : First made available on ORBilu
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	Focus Areas :	Computational Sciences
	To cite this reference:	http://hdl.handle.net/10993/31809

Title :	The Vanishing of Low-Dimensional Cohomology Groups of the Witt and the Virasoro algebra
Language :	English
Author, co-author :	Ecker, Jill Marie-Anne [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
	Schlichenmaier, Martin [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2017
Number of pages :	27
Peer reviewed :	No
Keywords :	[en] Witt algebra ; Lie algebra cohomology ; Deformations of algebras ; Virasoro algebra ; conformal field theory
Abstract :	[en] A proof of the vanishing of the first and the third cohomology groups of the Witt algebra with values in the adjoint module is given. The proofs given in the present article are completely algebraic and independent of any underlying topology. They are a generalization of the ones provided by Schlichenmaier, who proved the vanishing of the second cohomology group using purely algebraic methods. In the case of the third cohomology group though, extra difficulties arise and the involved proofs are distinctly more complicated.
Funders :	University of Luxembourg - UL
Target :	Researchers ; Students
Permalink :	http://hdl.handle.net/10993/31809
FnR project :	FnR ; FNR5707106 > Martin Schlichenmaier > QUANTMOD > Quantization Of Moduli Spaces > 01/09/2014 > 31/08/2017 > 2013

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