```
<<LieLink`
SetDefaultAlgebra["A2"]
LieTensor[{1, 0}, {1, 0}]
(* => {0,1} + {2,0} *)
```

You can download LieLink from github.com/teake/LieLink.
## Friday, September 13, 2013

### LieLink: a Mathematica interface for LiE

Ever wished that you could easily transfer you computations done in LiE to Mathematica? You now can with LieLink! LieLink is an small Mathematica package that interfaces with LiE, allowing you to directly execute LiE commands in Mathematica and get the result back. Here's an small example:

## Sunday, August 18, 2013

### xTras 1.2

After quite a bit of hard work, I'm proud to announce xTras 1.2! The main change over the 1.1 releases is that it now has built-in documentation. That means that when you enter for example ?AllContractions, there will be a nicely formatted message that informs you how to use AllContractions:

Pressing the blue >> link at the end of the message opens up the reference page of AllContractions in the documentation center:

All of the built-in documentation can also be found online, at http://www.xact.es/xtras/documentation/.

Besides the new documentation, there's a plethora of other changes under the hood. As always, see the changelog for more details.

All of the built-in documentation can also be found online, at http://www.xact.es/xtras/documentation/.

Besides the new documentation, there's a plethora of other changes under the hood. As always, see the changelog for more details.

## Thursday, May 30, 2013

### xTras v1.1.3

I've just posted a new version of my

As always, you can grab the newest version of xTras from its www.xact.es/xtras, or have a look at the changelog for all the new features.

*Mathematica*package xTras. It fixes a couple of bugs and introduces some new functions. One of these functions is MakeTraceless, which takes any tensorial expression and returns its traceless version. For example:In:The output uses the implicit symmetrizations of the SymManipulator package. But we can also symmetrize explicitly by expanding the symmetries:MakeTraceless[RiemannCD[-a,-b,-c,-d]]

Out: \( R_{abcd} + \frac{2 R \underset{1234}{Sym}(g_{ac} g_{bd})}{2 -3 d + d^2} + - \frac{4 \underset{1234}{Sym}(g_{bd} R_{ac})}{-2 + d} \)

In:Of course, this is just the Weyl tensor inToCanonical@ExpandSym@MakeTraceless[RiemannCD[-a, -b, -c, -d]]

Out: \(- \frac{g_{bd} R_{ac}}{-2 + d} + \frac{g_{bc} R_{ad}}{-2 + d} + \frac{g_{ad} R_{bc}}{-2 + d} - \frac{g_{ac} R_{bd}}{-2 + d} - \frac{g_{ad} g_{bc} R}{2 -3 d + d^2} + \frac{g_{ac} g_{bd} R}{2 -3 d + d^2} + R_{abcd} \)

*d*dimensions:In:Another new function is ConstructDDIs, which construct dimensional dependent identities (DDIs). Say we have a two-dimensional manifold. We can then ask for a list of all DDIs which have one curvature tensor and two free indices:Simplification@RiemannToWeyl@ExpandSym@MakeTraceless[RiemannCD[-a, -b, -c, -d]]

Out: \(W_{abcd} \)

In:It returns just one DDI, namely the vanishing of the Einstein tensor. This is well know fact, namely that gravity in two dimensions is purely topological, because the Einstein-Hilbert action is equal to the two-dimensional Euler density.ConstructDDIs[RiemannCD[a,b,c,d],IndexList[a,b]

Out: \({R^{ab} - \tfrac{1}{2} g^{ab} R} \)

As always, you can grab the newest version of xTras from its www.xact.es/xtras, or have a look at the changelog for all the new features.

## Friday, February 8, 2013

### The Weyl group of C4

Time for a pretty picture! It's the Weyl group of the finite Lie algebra

Although

*C*._{4}Although

*C*is 'only' 36 dimensional, its Weyl group is a bit bigger and has 384 elements. The pictures doesn't show the elements of the Weyl group though, but rather all possible connections between them. If you looks closely the black dots aren't dots -- they're points where are lots of lines meet._{4}## Thursday, January 31, 2013

### Coxeter planes

Here are a few nice Coxeter projections of representations of finite Lie algebras. If you don't know what a Coxeter projection is, or a finite Lie algebra for that matter, have a look at my PhD thesis (from which I took these pictures). Or, visit John Stembridge's website for more information and pictures.

Update: some of these pictures do not show the full representation, but only a subset.

Update: some of these pictures do not show the full representation, but only a subset.

The orbits of the two highest dominant weights of the

**1764**representation of A_{5}.
The orbits of the two highest dominant weights of the

**5985**representation of A_{17}.
The orbits of the two highest dominant weights of the

**442**representation of B_{6}.
The adjoint representation of B

_{19}.
The adjoint representation of D

_{10}.## Thursday, January 3, 2013

### Feynman's ode to a flower

Here's a beautiful animation by Fraser Davidson accompanying a soundbite from Richard Feynman. The soundbite is from a 1981 episode of BBC's Horizon, "The pleasure of finding things out", which, if you haven't seen it, I can wholeheartedly recommend.

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