What does it mean by the order of Casimir invariants - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-24T05:23:26Z http://mathoverflow.net/feeds/question/90398 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/90398/what-does-it-mean-by-the-order-of-casimir-invariants What does it mean by the order of Casimir invariants ciksalma 2012-03-06T21:22:26Z 2012-03-09T17:17:09Z <p>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. </p> <p>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 </p> <p>$C=J^{2}<em>{1}+J^{2}</em>{2}+J^{2}_{3}$.</p> <p>Also this is the center of the $\mathfrak{so}(3)$ algebra which commute with $J_{i}, i=1,2,3$. </p> <p>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? </p> <p>Thanks in advance N.B. I am a theoretical physicist with physics background and no formal pure maths knowledge.</p>