论文标题
普遍的海森贝格代数适用于对正交，洛伦兹和庞加雷代数及其双重扩展的实现
Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
论文作者
论文摘要
我们介绍了广义的Heisenberg代数$ \ MATHCAL {H} _n $，并在$ \ Mathcal {H} _N $的半完整中构建了Power系列对正交和Lorentz代数的实现。获得的实现是根据Bernoulli数字的生成函数给出的。我们还通过量子角度引入了正交和洛伦兹代数的扩展，并研究了$ \ Mathcal {h} _n $中扩展代数的实现。此外，我们表明，通过扩展广义的Heisenberg代数$ \ MATHCAL {H} _n $也可以通过量子角度获得对Poincare代数及其扩展的实现。
We introduce the generalized Heisenberg algebra $\mathcal{H}_n$ and construct realizations of the orthogonal and Lorentz algebras by power series in a semicompletion of $\mathcal{H}_n$. The obtained realizations are given in terms of the generating functions for the Bernoulli numbers. We also introduce an extension of the orthogonal and Lorentz algebras by quantum angles and study realizations of the extended algebras in $\mathcal{H}_n$. Furthermore, we show that by extending the generalized Heisenberg algebra $\mathcal{H}_n$ one can also obtain realizations of the Poincare algebra and its extension by quantum angles.
