Reduction (by stages) in the whole Lagrange–Poincaré category

$\def\LP{\mathfrak{LP}}$$\def\Link{\href{ https://books.google.com/books?id=mJXUCQAAQBAJ&lpg=PR7&ots=bp4aPKJ7nB&lr&pg=PR7#v=onepage&q&f=false}{[7]}}$We study the reduction scheme in the whole $\LP$ category, introduced in $\Link$ to perform Lagrangian reduction by stages. We answer affirmatively the open question of whether reduction can be done in the whole category. Furthermore, we analyze the Noether theorem on $\LP$-bundles, the relationship with Hamiltonian reduction by stages and some geometric aspects of the definition of this category.

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MAB has been partially supported by Ministerio de Educación by a FPU contract. MCL has been partially supported by Junta de Castilla y León, Spain, under grant no. SA090G19. Both authors have been partially supported by Agencia Nacional de Investigación, Spain, under grants no. PGC2018-098321-B-I00 and PID2021-126124NB-I00.

Published 5 January 2024