Descrição: I report the recent advances in applying (graded) Hopf algebras with braided tensor product in two scenarios: {\it i}) paraparticles beyond bosons and fermions living in any space dimensions and transforming under the permutation group; {\it ii}) physical models of anyons living in two space-dimensions and transforming under the braid group. In the first scenario simple toy models based on the so-called $2$-bit parastatistics show that, in the multiparticle sector, certain observables can discriminate paraparticles from ordinary bosons/fermions (thus, providing a counterexample to the widespread belief of the ``conventionality of parastatistics\cc~argument). In the second scenario the notion of (braided) Majorana qubit is introduced as the simplest building block to implement the Kitaev's proposal of a topological quantum computer which protects from decoherence.

Número: CBPF-NF-004/24