Although the determinate of that matrix = 0, and if it&#x27;s conjugate transpose determinant is non zero then I wonder if all valid possible configurations on this board can be represented by a complex lie group?<p>Edit: did the work, it does, but too lazy to describe the group <a href="https:&#x2F;&#x2F;gist.github.com&#x2F;cinquemb&#x2F;18e494348045725e2b60" rel="nofollow">https:&#x2F;&#x2F;gist.github.com&#x2F;cinquemb&#x2F;18e494348045725e2b60</a>