Title

Lie polynomial characterization problems

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Conference Proceeding

Source Title

Springer Proceedings in Mathematics and Statistics

Volume

317

First Page

593

Last Page

601

Publication Date

1-1-2020

Abstract

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.

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Digitial Object Identifier (DOI)

10.1007/978-3-030-41850-2_25

Disciplines

Mathematics

Keywords

Associative algebras; Lie algebras

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