Geodesic
Central Extensions, Derivations, and Automorphisms of Semi-Direct Sums of the Witt Algebra with its Intermediate Series Modules
Lucas Buzaglo1 ; Girish S. Vishwa2
1Department of Mathematics, University of California at San Diego, La Jolla, U.S.A.
2Maxwell Institute and School of Mathematics, The University of Edinburgh, Scotland, United Kingdom
Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 455-506

Voir la notice de l'article provenant de la source Heldermann Verlag

Lie algebras formed via semi-direct sums of the Witt algebra $\mathcal{W} = {\rm Der}(\mathbb{C}[t,t^{-1}])$ and its modules have become increasingly prominent in both physics and mathematics in recent years. In this paper, we complete the study of (Leibniz) central extensions, derivations and automorphisms of the Lie algebras formed from the semi-direct sum of the Witt algebra and its indecomposable intermediate series modules (that is, graded modules with one-dimensional graded components). Our techniques exploit the internal grading of the Witt algebra, which can be applied to a wider class of graded Lie algebras.
Classification : 17B40, 17B56, 17B65, 17B68
Mots-clés : Witt algebra, Virasoro algebra, intermediate series module, tensor density module, central extension, derivation, automorphism, Lie algebra cohomology, Leibniz cohomology

Lucas Buzaglo  1   ; Girish S. Vishwa  2

1 Department of Mathematics, University of California at San Diego, La Jolla, U.S.A.
2 Maxwell Institute and School of Mathematics, The University of Edinburgh, Scotland, United Kingdom 
Lucas Buzaglo; Girish S. Vishwa. Central Extensions, Derivations, and Automorphisms of Semi-Direct Sums of the Witt Algebra with its Intermediate Series Modules. Journal of Lie Theory, Tome 35 (2025) no. 3, pp. 455-506. http://geodesic.mathdoc.fr/item/JOLT_2025_35_3_a1/
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     title = {Central {Extensions,} {Derivations,} and {Automorphisms} of {Semi-Direct} {Sums} of the {Witt} {Algebra} with its {Intermediate} {Series} {Modules}},
     journal = {Journal of Lie Theory},
     pages = {455--506},
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