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Invariant conformal Killing forms on almost abelian Lie groups

Cecilia Herrera, Marcos Origlia

Abstract

We describe completely conformal Killing or conformal Killing-Yano (CKY) $p$-forms on almost abelian metric Lie algebras. In particular we prove that if a $n$-dimensional almost abelian metric Lie algebra admits a non-parallel CKY $p$-form, then $p=1$ or $p=n-1$. In other words, any CKY $p$-form on a metric almost abelian Lie algebra is parallel for $2\leq p\leq n-2$. Moreover, we characterize almost abelian Lie algebras admitting non-parallel CKY $p$-forms, and we classify all Lie algebras with this property up to dimension $5$, distinguishing also those cases where the associated simply connected Lie group admits lattices.

Invariant conformal Killing forms on almost abelian Lie groups

Abstract

We describe completely conformal Killing or conformal Killing-Yano (CKY) -forms on almost abelian metric Lie algebras. In particular we prove that if a -dimensional almost abelian metric Lie algebra admits a non-parallel CKY -form, then or . In other words, any CKY -form on a metric almost abelian Lie algebra is parallel for . Moreover, we characterize almost abelian Lie algebras admitting non-parallel CKY -forms, and we classify all Lie algebras with this property up to dimension , distinguishing also those cases where the associated simply connected Lie group admits lattices.
Paper Structure (11 sections, 35 equations, 3 tables)

This paper contains 11 sections, 35 equations, 3 tables.

Table of Contents

  1. Introduction
  2. CKY $p$-forms on Lie groups
  3. Preliminaries
  4. Almost abelian Lie groups
  5. Lattices in almost abelian Lie groups
  6. CKY $2$-forms
  7. $p$-forms on almost abelian Lie algebras
  8. CKY $p$-forms on almost abelian Lie algebras
  9. Low dimensional cases
  10. dimension $4$
  11. dimension $5$

Theorems & Definitions (10)

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