We deal with some matters needed to construct concrete left Hopf algebras for inhomogeneous quantum groups produced as noncommutative symmetries of fermionic and bosonic creation/annihilation operators. We find a map for the bidimensional fermionic case, produced as in Manin's [Quantum Groups and Non-commutative Hopf Geometry (CRM Univ. de Montréal, 1988)] seminal work, named preantipode that fulfills all the necessary requirements to be left but not right on the generators of the algebra. Due to the complexity and importance of the full task, we consider our result as an important step that will be extended in the near future.
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2012
American Institute of Physics
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