APURBA DAS
Articles written in Proceedings – Mathematical Sciences
Volume 129 Issue 1 February 2019 Article ID 0012 Research Article
Nambu structures and associated bialgebroids
SAMIK BASU SOMNATH BASU APURBA DAS GOUTAM MUKHERJEE
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.
Volume 129 Issue 4 September 2019 Article ID 0059 Research Article
Nambu structures on Lie algebroids and their modular classes
APURBA DAS SHILPA GONDHALI GOUTAM MUKHERJEE
We introduce the notion of the modular class of a Lie algebroid equipped with a Nambu structure. In particular, we recover the modular class of a Nambu-Poisson manifold $M$ with its Nambu tensor $\Lambda$ as the modular class of the tangent Lie algebroid $TM$ with Nambu structure $\Lambda$. We show that many known properties of the modular class of a Nambu-Poisson manifold and that of a Lie algebroid extend to the setting of a Lie algebroid with Nambu structure. Finally, we prove that for a large class of Nambu-Poisson manifolds considered as tangent Lie algebroids with Nambu structures, the associated modular classes are closely related to Evens-Lu-Weinstein modular classes of Lie algebroids.
Volume 130 All articles Published: 30 January 2020 Article ID 0020 Research Article
Gerstenhaber algebra structure on the cohomology of a hom-associative algebra
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. In this paper, we define a cup product on the cohomology of a hom-associative algebra. A direct verification shows that this cup product together with the degree−1 graded Lie bracket (which controls the deformation of the hom-associative algebra structure) on the cohomology makes it a Gerstenhaber algebra.
Volume 130, 2020
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