Prof. Grabowski has placed a review of the various brackets found in geometry and physics [1]. He also covers some of the ideas of superalgebra and graded differential geometry as many of the brackets really have their roots there. The review is based on a mini-course held at XXI Fall Workshops on Geometry and Physics, Burgos (Spain), 2012.

I have posted here about the review here as it contains a lot of the background material needed to understand my own research. In particular I am interested in brackets found in supergeometry, including super versions of Poisson, Jacobi and Loday brackets.

**Brackets?**

Rather generally, a bracket is understood as a non-associative operation on a vector space or a module. The principle example here is a Lie bracket. The review focuses on Lie brackets, such as Poisson and Jacobi brackets as well as Loday brackets, which are a non-skewsymmetric generalisation of a Lie bracket.

Interestingly, various forms of brackets arise in a wide context in contemporary mathematics. For example, Poisson brackets are found in classical and quantum mechanics as well as the theory of cluster algebras and geometric representation theory.

**Prof. Janusz Grabowski**

Prof Grabowski is Head of the Department of Mathematical Physics and Differential Geometry at the Institute of Mathematics within Polish Academy of Sciences. His personal homepage can be found here. |

**Reference**

[1] Janusz Grabowski, Brackets, arXiv:1301.0227 [math.DG], 2012.