On left Hopf algebras within the framework of inhomogeneous quantum groups for particle algebras

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 a...

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Bibliographic Details
Published in:Journal of mathematical physics 2012-10, Vol.53 (10), p.1
Main Author: Rodríguez-Romo, Suemi
Format: Article
Language:English
Subjects:
ALGEBRA
Algebraic group theory
ANNIHILATION OPERATORS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COMMUTATION RELATIONS
Exact sciences and technology
FERMIONS
Geometry
GROUP THEORY
Mathematical methods in physics
Mathematics
Physics
QUANTUM GROUPS
Quantum physics
Sciences and techniques of general use
SYMMETRY
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Summary: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.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.4754703