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A Clifford algebra is an associative algebra that generalizes the sequence R, C, H, etc. Filtrations are increasing chains of subspaces that respect the structure of the object they are filtering. In this paper, we filter ideals in Clifford algebras. These filtrations must also satisfy a “Clifford condition”, making them compatible with the algebra structure. We define a notion of equivalence between these filtered ideals and proceed to analyze the space of equivalence classes. We focus our attention on a specific class of filtrations, which we call principal filtrations. Principal filtrations are described by a single element in complex projective space and their equivalence classes are orbits of a group action inside complex projective space. In this paper, we identify when the space of equivalence classes of principal filtrations has a discrete topology or not. We find one example where the space of equivalence classes is not discrete, and is instead homeomorphic to S^2.
Bennett, Julia C., "Filtering Irreducible Clifford Supermodules" (2011). Senior Projects Spring 2011. 1.
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