University of Guilan Journal of Algebra and Related Topics 2345-3931 14 Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024). 2026 04 01 Generalized Reynolds operators and extensions of Lie-Yamaguti algebra bundle 139 159 9287 10.22124/jart.2025.32090.1871 EN S. Goswami Department of Mathematics, Ramakrishna Mission Vivekananda Educational and Research Institute, Howrah, India 0009-0005-7864-330X G. Mukherjee Academy of Scientific and Innovative Research (AcSIR), Ghaziabad, India Journal Article 2025 10 27 A Lie-Yamaguti algebra bundle is a type of algebra bundles with fibres being Lie-Yamaguti algebras, and appears naturally from geometric considerations in the work of M. Kikkawa. The aim of the present paper is to introduce the notion of generalized Reynolds operators, O-operators and Nijenhuis operators in the context of Lie-Yamaguti algebra bundle and find their applications. We also study abelian extensions of Lie-Yamaguti algebra bundles and investigate its relationship with its cohomology. https://jart.guilan.ac.ir/article_9287_3b7a8b99eaddbf23131a17a38166c1e0.pdf