Summary:
Given a holomorphic Lie algebroid (V,ø) on a compact connected Riemann surface X, we give a necessary and sufficient condition for a holomorphic vector bundle E on X to admit a holomorphic Lie algebroid connection. If (V,ø) is nonsplit, then every holomorphic vector bundle on X admits a holomorphic Lie algebroid connection for (V,ø). If (V,ø) is split, then a holomorphic vector bundle E on X admits a holomorphic Lie algebroid connection if and only if the degree of each indecomposable component of E is zero.
Keywords: Atiyah bundle; Split Lie algebroid; Nonsplit Lie algebroid; Connection
JCR-JIF Impact Factor and WoS quartile: 0,800 - Q2 (2025)
DOI reference:
https://doi.org/10.1016/j.jalgebra.2025.05.020
Published on paper: November 2025.
Published on-line: June 2025.
Citation:
D. Alfaya, I. Biswas, P. Kumar, A. Singh, "A criterion for holomorphic Lie algebroid connections", Journal of Algebra, Vol. 681, pp. 343 - 366, November 2025. [Online: June 2025] doi: 10.1016/j.jalgebra.2025.05.020
