\(q\)-deformation of the square white noise Lie algebra. (English) Zbl 1400.46057
Summary: For \(q \in(0, 1)\), the \(q\)-deformation of the square white noise Lie algebra is introduced using the \(q\)-calculus. A representation of this Lie algebra is given, using the \(q\)-derivative (or Jackson derivative) and the multiplication operator. The free square white noise Lie algebra is defined. Moreover, its representation on the Hardy space is given.
MSC:
| 46L65 | Quantizations, deformations for selfadjoint operator algebras |
| 17B99 | Lie algebras and Lie superalgebras |
| 60H40 | White noise theory |
Keywords:
\(q\)-derivative; \(q\)-square white noise Lie algebra; free square white noise Lie algebraReferences:
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