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arXiv · 1404.0464

On q-deformed infinite-dimensional n-algebra

Lu Ding·Xiao-Yu Jia·Ke Wu·Zhao-Wen Yan·Wei-Zhong Zhao
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Abstract

The $q$-deformation of the infinite-dimensional $n$-algebra is investigated. Based on the structure of the $q$-deformed Virasoro-Witt algebra, we derive a nontrivial $q$-deformed Virasoro-Witt $n$-algebra which is nothing but a sh-$n$-Lie algebra. Furthermore in terms of the pseud-differential operators on the quantum plane, we construct the (co)sine $n$-algebra and the $q$-deformed $SDiff(T^2)$ $n$-algebra. We prove that they are the sh-$n$-Lie algebras for the case of even $n$. An explicit physical realization of the (co)sine $n$-algebra is given.

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Lu Ding, Xiao-Yu Jia, Ke Wu, Zhao-Wen Yan, Wei-Zhong Zhao. 2014-04-02. On q-deformed infinite-dimensional n-algebra. https://arxiv.org/abs/1404.0464

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