A Clifford algebra is a weak Hopf algebra in a suitable symmetric monoidal category.
It is well known that Clifford algebras are group algebras deformed by a 2-cocyle. Furthermore, these algebras, which are not commutative in the usual sense, can be viewed as commutative algebras in certain symmetric monoidal categories of graded vector spaces. In this paper, the author shows that Clifford algebras have also cocommutative coalgebra structures, and consequently commutative and cocommutative weak braided Hopf algebra structures where they lie as commutative algebras. Furthermore, the author proves that all the Cayley-Dickson and Clifford weak braided Hopf algebras are selfdual weak braided Hopf algebras, monoidal Frobenius algebras and monoidal coFrobenius coalgebras within the symmetric monoidal categories of graded vector spaces where they reside.
scientific article; zbMATH DE number 5969527
scientific article