Lie polynomial characterization problems
College of Science
Mathematics and Statistics Department
Springer Proceedings in Mathematics and Statistics
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. © Springer Nature Switzerland AG 2020.
Digitial Object Identifier (DOI)
Cantuba, R., & Silvestrov, S. (2020). Lie polynomial characterization problems. Springer Proceedings in Mathematics and Statistics, 317, 593-601. https://doi.org/10.1007/978-3-030-41850-2_25
Associative algebras; Lie algebras