Added documentation fro Groups module

docs/make.jl

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+using Documenter
+
+import Pkg
+Pkg.activate("../")
+using LatticeGPU
+
+makedocs(sitename="LatticeGPU", modules=[LatticeGPU], doctest=true,
+         repo = "https://igit.ific.uv.es/alramos/latticegpu.jl")

docs/src/groups.md

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+
+# Groups and Algebras
+
+The module `Groups` contain generic data types to deal with group and
+algebra elements. Group elements $$g\in SU(N)$$ are represented in
+some compact notation. For the case $$N=2$$ we use two complex numbers
+(Caley-Dickson representation, i.e. $$g=(z_1,z_2)$$ with
+$$|z_1|^2 + |z_2|^2=1$$). For the case $$N=3$$ we only store two
+rows of the $$N\times N$$ unitary matrix.
+
+Group operations translate straightforwardly in matrix operations,
+except for $$SU(2)$$, where we use
+```math
+\forall g=(z_1, z_2)\in SU(2)\, \Longrightarrow\, g^{-1} =
+(\overline z_1, -z_2)
+```
+and 
+```math
+\forall g=(z_1, z_2), g'=(w_1,w_2)\in SU(2)\, \Longrightarrow \, g g'= (z_1w_1 - \overline w_2 z_2, w_2z_1 + z_2\overline w_1)\,.
+```
+
+Group elements can be "casted" into arrays. The abstract type
+[`GMatrix`](@ref) represent generic $$ N\\times N$$ complex arrays.
+
+
+Algebra elements $$X \in \mathfrak{su}(N)$$ are traceless
+anti-hermitian matrices represented trough $$N^2-1$$ real numbers
+$$X^a$$. We have
+```math
+  X = \sum_{a=1}^{N^2-1} X^a T^a
+```
+where $$T^a$$ are a basis of the $$\mathfrak{su}(N)$$ algebra with
+the conventions
+```math
+  (T^a)^+ = -T^a \,\qquad
+  {\rm Tr}(T^aT^b) = -\frac{1}{2}\delta_{ab}\,.
+```
+
+If we denote by $$\{\mathbf{e}_i\}$$ the usual ortonormal basis of
+$$\mathbb R^N$$, the $$N^2-1$$ matrices $$T^a$$ can always be written in the
+following way 
+1. symmetric matrices ($$N(N-1)/2$$) 
+   ```math
+   (T^a)_{ij} = \frac{\imath}{2}(\mathbf{e}_i\otimes\mathbf{e}_j +
+   \mathbf{e}_j\otimes \mathbf{e}_i)\quad (1\le i < j \le N)
+   ```
+1. anti-symmetric matrices ($$N(N-1)/2$$) 
+   ```math
+   (T^a)_{ij} = \frac{1}{2}(\mathbf{e}_i\otimes\mathbf{e}_j -
+   \mathbf{e}_j\otimes \mathbf{e}_i)\quad (1\le i < j \le N)
+   ```
+1. diagonal matrices ($$N-1$$). With $$l=1,...,N-1$$ and $$a=l+N(N-1)$$
+   ```math
+   (T^a)_{ij} = \frac{\imath}{2}\sqrt{\frac{2}{l(l+1)}}
+   \left(\sum_{j=1}^l\mathbf{e}_j\otimes\mathbf{e}_j -
+     l\mathbf{e}_{l+1}\otimes \mathbf{e}_{l+1}\right)
+   \quad (l=1,\dots,N-1;\, a=l+N(N-1))
+   ```
+
+For example in the case of $$\mathfrak{su}(2)$$, and denoting the Pauli
+matrices by $$\sigma^a$$ we have
+```math
+  T^a = \frac{\imath}{2}\sigma^a \quad(a=1,2,3)\,,
+```
+while for $$\mathfrak{su}(3)$$ we have $$T^a=\imath \lambda^a/2$$ (with
+$$\lambda^a$$ the Gell-Mann matrices) up to a permutation.
+
+
+## Some examples
+
+```@setup exs
+import Pkg # hide
+Pkg.activate("/home/alberto/code/julia/LatticeGPU/") # hide
+using LatticeGPU # hide
+```
+
+Here we just show some example codes playing with groups and
+elements. The objective is to get an idea on how group operations 
+We can generate some random group elements.
+```@repl exs
+# Generate random groups elements, 
+# check they are actually from the grup
+g = rand(SU2{Float64})
+println("Are we in a group?: ", isgroup(g))
+g = rand(SU3{Float64})
+println("Are we in a group?: ", isgroup(g))
+```
+
+We can also do some simple operations 
+```@repl exs
+X = rand(SU3alg{Float64})
+g1 = exp(X);
+g2 = exp(X, -2.0); # e^{-2X}
+g = g1*g1*g2;
+println("Is this one? ", dev_one(g))
+```
+
+## Types 
+
+### Groups
+
+The generic interface reads
+
+```@docs
+Group
+```
+
+Concrete supported implementations are
+```@docs
+SU2
+SU3
+```
+
+### Algebras
+
+The generic interface reads
+```@docs
+Algebra
+```
+
+With the following concrete implementations
+```@docs
+SU2alg
+SU3alg
+```
+
+### GMatrix
+
+The generic interface reads
+```@docs
+GMatrix
+```
+
+With the following concrete implementations
+```@docs
+M2x2
+M3x3
+```
+
+
+## Generic `Group` methods
+
+```@docs
+inverse
+dag
+tr
+dev_one
+unitarize
+isgroup
+projalg
+```
+
+## Generic `Algebra` methods
+
+```@docs
+exp
+expm
+alg2mat
+```
+
+

docs/src/index.md

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+
+# LatticeGPU.jl documentation
+
+
+```@contents
+```
+
+