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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| Main Authors: | , |
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| Format: | text |
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Animo Repository
2020
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| Online Access: | https://animorepository.dlsu.edu.ph/faculty_research/1996 |
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| Institution: | De La Salle University |
| Summary: | 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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