The lattice of H-prime ideals of O_{q}(M_{2}(k)) is displayed below. The symbols • and ∘ stand for generators X_{ij} which are or are not included in a given prime, and □ stands for the 2 × 2 quantum determinant. For example, \binom{∘•}{•∘} stands for the ideal ⟨X_{12}, X_{21}⟩, and (□) stands for the ideal ⟨X_{11}X_{22} − qX_{12}X_{21}⟩.

The corresponding H-strata in spec O_{q}(M_{2}(k)) can be easily calculated. For instance, if q is not a root of unity, the strata corresponding to \binom{∘∘}{∘∘} and \binom{∘•}{•∘} are 2-dimensional, the strata corresponding to \binom{••}{∘•}, \binom{••}{•∘}, \binom{∘•}{••}, and \binom{•∘}{••} are all 1-dimensional, and the remaining 8 strata are singletons.

[figure: \binom{••}{••}; _{\binom{••}{∘•}}; _{\binom{••}{•∘}}; _{\binom{∘•}{••}}; _{\binom{•∘}{••}}; _{\binom{••}{∘∘}}; _{\binom{∘•}{∘•}}; _{\binom{∘•}{•∘}}; _{\binom{•∘}{•∘}}; _{\binom{∘∘}{••}}; _{\binom{∘•}{∘∘}}; (□); _{\binom{∘∘}{•∘}}; _{\binom{∘∘}{∘∘}}; H-spec O_{q}(M_{2}(k))]

(This is taken from the paper “Prime ideals in certain quantum determinantal rings” by K R Goodearl and T H Lenagan.)