• Nambu structures and associated bialgebroids

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/129/01/0012

• # Keywords

$n$-Ary operation; Nambu–Poisson bracket; Gerstenhaber bracket; Lie bialgebroid

• # Abstract

We investigate higher-order generalizations of well known results for Liealgebroids and bialgebroids. It is proved that $n$-Lie algebroid structures correspond to $n$-ary generalization of Gerstenhaber algebras and are implied by $n$-ary generalization of linear Poisson structures on the dual bundle. A Nambu–Poisson manifold (of order $n$ > 2) gives rise to a special bialgebroid structure which is referred to as a weak Lie–Filippov bialgebroid (of order $n$). It is further demonstrated that such bialgebroids canonically induce a Nambu–Poisson structure on the base manifold. Finally, the tangent space of a Nambu Lie group gives an example of a weak Lie–Filippov bialgebroid over a point.

• # Author Affiliations

1. Stat-Math Unit, Indian Statistical Institute, Kolkata 700 108, India
2. Department of Mathematics and Statistics, Indian Institute of Science Education and Research, Mohanpur 741 246, India

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019