Some Homological Properties Of The Standard Podle(?) Sphere

In this paper, we study the homological properties of the standard Podles sphere. We first consider the relation between gl. dim B and gl. dim A where B C A is a quan-tum homogeneous space. Then, we prove that the global dimension of the standard Podles sphere is 2. By using the grading-lifting technique, we prove that the standard Podles sphere is an Aulander-regular and Cohen-Macaulay algebra. In the end, we show that the Ext-algebra of the standard Podles sphere is a graded Frobenius algebra. The Nakayama automorphism of the Frobenius algebra is also given.