Lie polynomial characterization problems
We present a review of some results about Lie polynomials in finitely-generated associative algebras with defining relations that involve deformed commutation relations. Such algebras have arisen from various areas such as in the theory of quantum groups, of q-oscillators, of q-deformed Heisenberg a...
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oai:animorepository.dlsu.edu.ph:faculty_research-29952023-10-28T07:48:06Z Lie polynomial characterization problems Cantuba, Rafael Reno S. Silvestrov, Sergei We present a review of some results about Lie polynomials in finitely-generated associative algebras with defining relations that involve deformed commutation relations. Such algebras have arisen from various areas such as in the theory of quantum groups, of q-oscillators, of q-deformed Heisenberg algebras, of orthogonal polynomials, and even from algebraic combinatorics. The q-deformed Heisenberg-Weyl relation is so far the most successful setting for a Lie polynomial characterization problem. Both algebraic and operator-theoretic approaches have been found. We also discuss some partial results for other algebras related to quantum groups. 2020-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/faculty_research/1996 info:doi/10.1007/978-3-030-41850-2_25 Faculty Research Work Animo Repository Lie algebras Polynomials Associative algebras Mathematics |
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Philippines Philippines |
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Lie algebras Polynomials Associative algebras Mathematics |
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Lie algebras Polynomials Associative algebras Mathematics Cantuba, Rafael Reno S. Silvestrov, Sergei Lie polynomial characterization problems |
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We present a review of some results about Lie polynomials in finitely-generated associative algebras with defining relations that involve deformed commutation relations. Such algebras have arisen from various areas such as in the theory of quantum groups, of q-oscillators, of q-deformed Heisenberg algebras, of orthogonal polynomials, and even from algebraic combinatorics. The q-deformed Heisenberg-Weyl relation is so far the most successful setting for a Lie polynomial characterization problem. Both algebraic and operator-theoretic approaches have been found. We also discuss some partial results for other algebras related to quantum groups. |
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text |
| author |
Cantuba, Rafael Reno S. Silvestrov, Sergei |
| author_facet |
Cantuba, Rafael Reno S. Silvestrov, Sergei |
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Cantuba, Rafael Reno S. |
| title |
Lie polynomial characterization problems |
| title_short |
Lie polynomial characterization problems |
| title_full |
Lie polynomial characterization problems |
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Lie polynomial characterization problems |
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Lie polynomial characterization problems |
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lie polynomial characterization problems |
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Animo Repository |
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2020 |
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https://animorepository.dlsu.edu.ph/faculty_research/1996 |
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1781799775760285696 |