ɪf ɪz ðə lˈaɪ ˈældʒᵻbɹə , ðˈɛn ðə sˈɛntɚɹ ʌvðə jˌuːnɪvˈɜːsəl ɛnvˈɛləpɪŋ ˈældʒᵻbɹə ɪz dʒˈɛnɚɹˌeɪɾᵻd baɪ ðə kˈæsɪmˌɪɹ ɪnvˈɛɹiənt ʌv dᵻɡɹˈiː tˈuː, ænd ðə wˈeɪl ɡɹˈuːp ˈækts ɔnðə kˈɑːɹtən sˈʌbɐldʒˌɛbɹə, wˌɪtʃ ɪz ˌaɪsəmˈoːɹfɪk tuː , baɪ nᵻɡˈeɪʃən, sˌoʊ ðɪ ɪnvˈɛɹiənt ʌvðə wˈeɪl ɡɹˈuːp ɪz ðə skwˈɛɹ ʌvðə dʒˈɛnɚɹˌeɪɾɚɹ ʌvðə kˈɑːɹtən sˈʌbɐldʒˌɛbɹə, wˌɪtʃ ɪz ˈɔːlsoʊ ʌv dᵻɡɹˈiː tˈuː.
If  is the Lie algebra , then the center of the universal enveloping algebra is generated by the Casimir invariant of degree 2, and the Weyl group acts on the Cartan subalgebra, which is isomorphic to , by negation, so the invariant of the Weyl group is the square of the generator of the Cartan subalgebra, which is also of degree 2.