Journal of Lie Theory

no. 3
Central Extensions, Derivations, and Automorphisms of Semi-Direct Sums of the Witt Algebra with its Intermediate Series Modules
Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 455-506
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.
DOI: 10.5802/jolt.1393
Classification: 17B40, 17B56, 17B65, 17B68
Keywords: Witt algebra, Virasoro algebra, intermediate series module, tensor density module, central extension, derivation, automorphism, Lie algebra cohomology, Leibniz cohomology 
@article{JOLT_2025_35_3_a1,
     author = {L. Buzaglo and G. S. Vishwa},
     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},
     year = {2025},
     volume = {35},
     number = {3},
     doi = {10.5802/jolt.1393},
     zbl = {08103098},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1393/}
}
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%A G. S. Vishwa
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L. Buzaglo; G. S. Vishwa. Central Extensions, Derivations, and Automorphisms of Semi-Direct Sums of the Witt Algebra with its Intermediate Series Modules. Journal of Lie Theory, Volume 35 (2025) no. 3, pp. 455-506. doi: 10.5802/jolt.1393

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