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A Realization of the $W_{1+\infty}$ Algebra and Its $n$-Algebra |
| Chun-Hong Zhang, Rui Wang, Ke Wu, Wei-Zhong Zhao** |
School of Mathematical Sciences, Capital Normal University, Beijing 100048
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| Cite this article: |
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Chun-Hong Zhang, Rui Wang, Ke Wu et al 2017 Chin. Phys. Lett. 34 080202 |
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Abstract We consider a realization of the $W_{1+\infty}$ algebra and investigate its $n$-algebra, which is different from the $n$-algebra of Zhang et al. [2016 arXiv:1606.07570v2] It is found that the generators $W_m^{s}$ with any fixed superindex $s\geqslant 1$ yield the null sub-$2s$-algebra. The nontrivial sub-$4$-algebra and Virasoro–Witt $3$-algebra are presented. Moreover, we extend the generators to the multi-variables case. These generators also yield the $W_{1+\infty}$ algebra and null $n$-algebras.
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Received: 13 April 2017
Published: 22 July 2017
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| PACS: |
02.20.Tw
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(Infinite-dimensional Lie groups)
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02.30.Ik
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(Integrable systems)
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11.25.Hf
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(Conformal field theory, algebraic structures)
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| Fund: Supported by the National Natural Science Foundation of China under Grant Nos 11375119 and 11475116. |
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