What does it mean by the order of Casimir invariants

2012-03-06T21:22:26Z

I am now trying to understand my new set of Lie algebra. I am deforming the $\mathfrak{so}(3)$ algebra using the ordinary boson operator. The new algebra is 4-dimensional i.e. 4 generators.

As we all know, for $\mathfrak{so}(3)$, we have 3 generators satisfying $[J_{i}, J_{j}]= i\varepsilon_{ijk}J_{k}$. In addition to that we have a single independent Casimir. Symbolically, the Casimir is

$C=J^{2}{1}+J^{2}{2}+J^{2}_{3}$.

Also this is the center of the $\mathfrak{so}(3)$ algebra which commute with $J_{i}, i=1,2,3$.

For my new algebra, I have found that there are two type of Casimir which are independent with each other. Despite knowing that I have two-dimensional center(is this term correct?), what other information can I get from the Casimir?

Thanks in advance N.B. I am a theoretical physicist with physics background and no formal pure maths knowledge.

What does it mean by the order of Casimir invariants - MathOverflow [closed]

What does it mean by the order of Casimir invariants