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Local derivation on the Schr{ö}dinger Lie algebra in $(n+1)$-dimensional space-time

Alauadinov A. K., Yusupov B. B

Abstract

This paper studies local derivations on the Schr{ö}dinger algebra $\ms_n$ in $(n+1)$-dimensional space-time of Schr{ö}dinger Lie groups for any integer $n$. The purpose of this work is to prove that every local derivation on $\ms_n$ is a derivation.

Local derivation on the Schr{ö}dinger Lie algebra in $(n+1)$-dimensional space-time

Abstract

This paper studies local derivations on the Schr{ö}dinger algebra in -dimensional space-time of Schr{ö}dinger Lie groups for any integer . The purpose of this work is to prove that every local derivation on is a derivation.
Paper Structure (3 sections, 8 theorems, 64 equations)

This paper contains 3 sections, 8 theorems, 64 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main results

Key Result

Theorem 2.3

The derivations of the Schrödinger algebra $\mathfrak{s}_n$ are given by where $\sigma_1,\tau,\sigma$ are given by Definition def1.

Theorems & Definitions (17)

  • Definition 2.1
  • Definition 2.2
  • Theorem 2.3
  • Example 2.4
  • Theorem 3.1
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • ...and 7 more