## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- The Japanese-Australian Workshop on Real and Complex Singularities: JARCS III. Toshizumi Fukui, Adam Harris, Alexander Isaev, Satoshi Koike and Laurentiu Paunescu, eds. Proceedings of the Centre for Mathematics and its Applications, v. 43. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 2010), 1 - 7

### Symmetry Via Lie Algebra Cohomology

#### Abstract

The Killing operator on a Riemmanian manifold is a linear differetial operator on vector fields whose kernel provides the infinitesimal Riemannian symmetries. The Killing operator is best understood in terms of its prolongation, which entails some simple tensor identities. These simple identities can be viewed as arising from the vanishing of certain Lie algebra cohomologies. The point is that this case provides a model for other more complicated operators similiarly concerned with symmetry.

#### Article information

**Dates**

First available in Project Euclid:
18 November 2014

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416320992

**Mathematical Reviews number (MathSciNet)**

MR2763231

**Zentralblatt MATH identifier**

1230.58025

#### Citation

Eastwood, Michael. Symmetry Via Lie Algebra Cohomology. The Japanese-Australian Workshop on Real and Complex Singularities: JARCS III, 1--7, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 2010. https://projecteuclid.org/euclid.pcma/1416320992