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- Title
Lie polynomials in an algebra defined by a linearly twisted commutation relation.
- Abstract
We present an elementary approach to characterizing Lie polynomials on the generators A , B of an algebra with a defining relation in the form of a twisted commutation relation A B = σ (B A). Here, the twisting map σ is a linear polynomial with a slope parameter, which is not a root of unity. The class of algebras defined as such encompasses q -deformed Heisenberg algebras, rotation algebras, and some types of q -oscillator algebras, the deformation parameters of which, are not roots of unity. Thus, we have a general solution for the Lie polynomial characterization problem for these algebras.
- Subjects
LIE algebras; RELATION algebras; ALGEBRA
- Publication
Journal of Algebra & Its Applications, 2022, Vol 21, Issue 9, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498822501754