Some Quantum-like Hopf Algebras which Remain Noncommutative when q = 1 |
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Authors: | Rodríguez-Romo Suemi Taft Earl |
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Institution: | (1) Centro de Investigaciones Teóricas, Universidad Nacional Autónoma de México, Campus Cuautitlán, Apdo, Postal 142, Cuautitlán Izcalli, Edo. de México, 54740, México;(2) Department of Mathematics, Rutgers, The State University of New Jersey, 110 Frelinghuysen Rd, Piscataway, NJ, 08854-8019, U.S.A. |
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Abstract: | Starting with only three of the six relations defining the standard (Manin) GL
q
(2), we try to construct a quantum group. The antipode condition requires some new relations, but the process stops at a Hopf algebra with a Birkhoff–Witt basis of irreducible monomials. The quantum determinant is group-like but not central, even when q = 1. So, the two Hopf algebras constructed in this way are not isomorphic to the Manin GL
q
(2), all of whose group-like elements are central. Analogous constructions can be made starting with the Dipper–Donkin version of GL
q
(2), but these turn out to be included in the two classes of Hopf algebras described above. |
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Keywords: | Hopf algebras quantum groups |
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