chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2021-22-1-273-291cheb-946Research ArticleСтатьиArticleСлабые алгебры Фаддеева — Тахтаджана — Волкова. Решеточные 𝑊𝑛 алгебрыWeak Faddeev–Takhtajan–Volkov algebras. Lattice 𝑊𝑛 algebrasРазавиниаФаррохRazaviniaFarrokhf.razavinia@phystech.eduМосковский физико-технический институтРоссияMoscow Institute of Physics and TechnologyRussian Federation202106042021221273291Copyright © Разавиниа Ф., 20212021Разавиниа Ф.Razavinia F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/946

В этой статье мы начнем с обсуждения исторического общего вида нашего проекта, а затем попытаемся построить новую скобку Пуассона на нашем простейшем примере 𝑠𝑙2, а затем попытаемся дать универсальную конструкцию на основе наших универсальных переменных, а затем постараемся построить решеточные 𝑊2-алгебры, которые будут игратьключевую роль в других наших конструкциях на решетчатых 𝑊3-алгебрах, и, наконец, мы попытаемся найти единственный нетривиальный зависимый генератор наших решеточных 𝑊4-алгебр и т. д. для решетки 𝑊𝑛-алгебры.

In this paper, we will start by deliberating at our project’s historical general view and then we will try to construct a new Poisson bracket on our simplest example 𝑠𝑙2 and then we will tryto give a universal construction based on our universal variables and then will try to construct lattice 𝑊2 algebras which will play a key role in our other constructions on lattice 𝑊3 algebrasand finally we will try to find the only nontrivial dependent generator of our lattice 𝑊4 algebras and so on for lattice 𝑊𝑛 algebras

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The authors declare that there are no conflicts of interest present.