Weak Faddeev-Takhtajan-Volkov algebras; Lattice $W_n$-algebras - дипломная работа | ИСТИНА – Интеллектуальная Система Тематического Исследования НАукометрических данных

Научный руководитель: Белов Алексей Яковлевич
Автор: Farrokh Razavinia
Тип: Магистр
Организация, в которой проходила защита: МФТИ
Год защиты: 2017
Аннотация: In this thesis, we will introduce a new and a weaker version of the famous Faddeev-Takhtajan-Volkov algebra in $Sl_2$ case and a complete calculation toward it by getting help of a new defined Poisson bracket just by using the Cartan matrix $A_2$ and then by employing this structure we will extend it to the $Sl_3$ case and so on to $Sl_n$ case by using the Cartan matrix $A_n$.\\ These newly defined structures will also help us to define Lattice $W_n$- algebras as an extension of Lattice Virasoro algebras in a very simple way which has known till now by employing Feigin's homomorphisms and screening operators and also our newly defined Poisson brackets; just based on the generators of the invariant space of the nilpotent part of $U_q(Sl_n)$.\\ Also, our approach gives an efficient way of solving system of partial differential equations in higher dimension with coefficients as functions consist of $n$ independent variables $X_1 , \cdots , X_n$ such that do not contain the unknown function $f$ as a solution, by transferring some results and ideas from "Chapter V, Section IV of Goursat's Differential Equations" in the language of Mathematica.
Добавил в систему: Белов Алексей Яковлевич

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