Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Automorphisms of Multiplicative Lie algebra Extensions

Dev Karan Singh, Shiv Datt Kumar

Abstract

In this paper, we discuss the inducibility problem for automorphisms of multiplicative Lie algebra extensions and show that obstruction to the inducibility of pairs lies in the second cohomology group of multiplicative Lie algebras. We also establish the Wells type exact sequence for multiplicative Lie algebras, which relates automorphism groups with the second cohomology group of multiplicative Lie algebras.

Automorphisms of Multiplicative Lie algebra Extensions

Abstract

In this paper, we discuss the inducibility problem for automorphisms of multiplicative Lie algebra extensions and show that obstruction to the inducibility of pairs lies in the second cohomology group of multiplicative Lie algebras. We also establish the Wells type exact sequence for multiplicative Lie algebras, which relates automorphism groups with the second cohomology group of multiplicative Lie algebras.
Paper Structure (3 sections, 15 theorems, 46 equations)

This paper contains 3 sections, 15 theorems, 46 equations.

Table of Contents

  1. Introduction
  2. Exact Sequences and Inducibility of a pair of Automorphisms
  3. Wells type exact sequence and  Inducible problem

Key Result

Lemma 2.1

If $\phi \in \text{Aut}_H(G)$, then the map $\eta$ does not depend on the choice of the transversal $t$.

Theorems & Definitions (29)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof
  • Remark 2.3
  • Remark 2.4
  • Corollary 2.5
  • Lemma 2.6
  • Lemma 3.1
  • proof
  • ...and 19 more