Filtered Clifford $\mathcal A$-algebras and orthogonal sums

Presenter: Patrice Ntumba, University of Pretoria, South Africa

Joint work with B. Yizengaw

In this talk, given an algebra sheaf $\mathcal A$ on a topological space $X$, we introduce sheaves of Clifford $\mathcal A$-algebras (Clifford $\mathcal A$-algebras, for short) on $X$ associated with arbitrary quadratic $\mathcal A$-modules as quotient sheaves of tensor algebra sheaves over certain ideal sheaves. We also study two main $\mathcal A$-isomorphisms of Clifford $\mathcal A$-algebras: the main involution and the anti-involution $\mathcal A$-isomorphisms. Finally, we give a definition for the natural filtration of Clifford $\mathcal A$-algebras and show that for every $\mathcal A$-algebra sheaf $\mathcal E$, endowed with a regular filtration, one obtains a new graded $\mathcal A$-algebra sheaf, denoted $Gr(\mathcal{E})$, which turns out to be $\mathcal A$-isomorphic to $\mathcal E$.