arXiv subjects
Publications and source records attributed to Deepak Pal.
In this paper, we develop the extension theory of commutative Poisson algebras. Specifically, we define the second cohomology of a commutative Poisson algebra $K$ with coefficients in an abelian Poisson algebra $H$. We then establish a natural bijective correspondence between this cohomology group and the set of equivalence classes of a special type of extensions.
This paper explores the properties of multiplicative Lie algebra structures on a nilpotent group of class $2$. We also present a method for determining a multiplicative Lie algebra structure on a group that serves as an extension of one Lie ring by another Lie ring such as a metacyclic group and a nilpotent group of class $2$.
In this article, we discuss Lie nilpotency and Lie solvability of non-abelian tensor product of multiplicative Lie algebras. In particular, for giving information concerning the Lie nilpotency (or Lie solvability) of either multiplicative Lie algebras $G$ or $H,$ the non-abelian tensor product $ \frac{G\otimes H}{I}$ is Lie nilpotent (or Lie solvable), for some ideal $I$ of ${G\otimes H}$.
The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.
The main aim of the article is to find the Schur multiplier and the Lie exterior square of some finite multiplicative Lie algebras. For a non abelian simple group $K$ with trivial Schur multiplier, we see that the Schur multiplier of multiplicative Lie algebra $K$ is trivial and the Lie exterior square of $K$ is an improper multiplicative Lie algebra $K.$