Abstract
A regular algebra of global dimension n+1 is often called a quantum ℙn. In 2011, Nafari, Vancliff and Zhang showed that graded skew Clifford algebras (GSCAs) could be used to classify most quadratic quantum ℙ2s. Some time later, Chandler, Tomlin and Vancliff used their work with certain families of GSCAs to develop a conjecture on the quantum space of a generic quadratic quantum ℙ3. These results suggest that (the isomorphism classes of) GSCAs are likely to play a fundamental role in the classification of quadratic quantum ℙ3s. In this article, we will discuss some of these results on GSCAs and discuss new results on isomorphisms between GSCAs.
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