Antisymmetrically deformed quantum homogeneous spaces (Q854372)

The author defines a \(\theta\)-deformation of the complex projective space. This is defined as the coinvariant subalgebra of the (quantum algebra of functions of) \(\theta\)-deformed quantum unitary group. Here \(\theta\) is an antisymmetric matrix of parameters. It is shown that the Hochschild dimension of the constructed \(\theta\)-deformed complex projective space \(C(\mathbb{C} P^{n-1}_\theta)\) is the same as the classical dimension of the undeformed complex projective space \(\mathbb{C} P^{n-1}\).