Some quantum-like Hopf algebras which remain noncommutative when \(q=1\). (Q1863695)
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scientific article; zbMATH DE number 1880347
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some quantum-like Hopf algebras which remain noncommutative when \(q=1\). |
scientific article; zbMATH DE number 1880347 |
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Some quantum-like Hopf algebras which remain noncommutative when \(q=1\). (English)
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12 March 2003
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The authors construct a quantum group using only three of the six relations defining the standard quantum group \(\text{GL}_q(2)\). They show that the quantum determinant of the obtained quantum group is group-like but not central, i.e. it does not commute with the matrix elements of the quantum group, and so the two Hopf algebras constructed in this way are not isomorphic to the standard quantum group.
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Hopf algebras
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quantum groups
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antipodes
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Birkhoff-Witt bases
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irreducible monomials
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quantum determinants
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group-like elements
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