Polynomial relations in the Heisenberg algebra. (English) Zbl 0823.17012
The nonlinear polynomial relations between the elements of the universal enveloping algebra of the Heisenberg algebra are investigated. Some relations hold after \(q\)-deformation. The existence of these relations simplifies the solution of the problem of the ordering of polynomials in creation/annihilation operators.
Reviewer: Ma Zhong-Qi (Beijing)
MSC:
| 17B35 | Universal enveloping (super)algebras |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
| 17B37 | Quantum groups (quantized enveloping algebras) and related deformations |
Keywords:
\(q\)-deformation; nonlinear polynomial relations; universal enveloping algebra; Heisenberg algebraDigital Library of Mathematical Functions:
§13.3(ii) Differentiation Formulas ‣ §13.3 Recurrence Relations and Derivatives ‣ Kummer Functions ‣ Chapter 13 Confluent Hypergeometric Functions§15.5(i) Differentiation Formulas ‣ §15.5 Derivatives and Contiguous Functions ‣ Properties ‣ Chapter 15 Hypergeometric Function
§16.3(i) Differentiation Formulas ‣ §16.3 Derivatives and Contiguous Functions ‣ Generalized Hypergeometric Functions ‣ Chapter 16 Generalized Hypergeometric Functions and Meijer 𝐺-Function
References:
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| [3] | DOI: 10.1088/0305-4470/27/2/002 · Zbl 0829.39001 · doi:10.1088/0305-4470/27/2/002 |
| [4] | DOI: 10.1016/0920-5632(91)90143-3 · doi:10.1016/0920-5632(91)90143-3 |
| [5] | DOI: 10.1016/0920-5632(91)90143-3 · doi:10.1016/0920-5632(91)90143-3 |
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