| 1. |
- Cantuba, Rafael Reno, et al.
(author)
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Lie polynomial characterization problems
- 2020
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In: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 ; , s. 593-601
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Book chapter (peer-reviewed)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.
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| 2. |
- Cantuba, Rafael Reno, et al.
(author)
-
Torsion-type q-deformed heisenberg algebra and its lie polynomials
- 2020
-
In: Algebraic Structures and Applications. - Cham : Springer Nature. - 9783030418496 ; , s. 575-592
-
Book chapter (peer-reviewed)abstract
- Given a scalar parameter q, the q-deformed Heisenberg algebra H(q) is the unital associative algebra with two generators A, B that satisfy the q-deformed commutation relation AB-qBA=I, where I is the multiplicative identity. For H(q) of torsion-type, that is if q is a root of unity, characterization is obtained for all the Lie polynomials in A, B and basis and graded structure and commutation relations for associated Lie algebras are studied.
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