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Lie nilpotency and Lie solvability of tensor product of multiplicative Lie algebras

Deepak Pal, Amit Kumar, Sumit Kumar Upadhyay, Seema Kushwaha

Abstract

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 ${G\otimes H}$.

Lie nilpotency and Lie solvability of tensor product of multiplicative Lie algebras

Abstract

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 or the non-abelian tensor product is Lie nilpotent (or Lie solvable), for some ideal of .
Paper Structure (5 sections, 16 theorems, 20 equations)

This paper contains 5 sections, 16 theorems, 20 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Tensor product of groups
  4. Tensor product of multiplicative Lie algebras
  5. On the nilpotency and solvability of tensor products

Key Result

Proposition 2.1

MRS Let $G$ be a multiplicative Lie algebra. Then following identities holds:

Theorems & Definitions (37)

  • Definition 2.1
  • Definition 2.2
  • Proposition 2.1
  • Definition 2.3
  • Definition 2.4
  • Proposition 2.2
  • Proposition 2.3
  • Definition 2.5
  • Definition 2.6
  • Proposition 2.4
  • ...and 27 more