Enumerations of Ideals in Niltriangular Subalgebra of Chevalley Algebras
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https://elib.sfu-kras.ru/handle/2311/71598Author:
Hodyunya, Nikolay D.
Ходюня, Николай Д.
Date:
2018-06Journal Name:
Журнал Сибирского федерального университета. Математика и физика. Journal of Siberian Federal University. Mathematics & Physics;2018 11 (3)Abstract:
Let N (K) be the niltriangular subalgebra of Chevalley algebra over a field K associated with a root
system . We consider certain non-associative enveloping algebras for some Lie algebra N (K). We
also study the problem of enumeration of standard ideals in algebra N (K) over any finite field K; for
classical Lie types this is the problem which was written earlier (2001). В работе Г. П. Егорычева и В. М. Левчука 2001 г. была записана проблема 1, заключающаяся в пе-
речислении стандартных идеалов нильтреугольных подалгебр N (GF(q)) алгебр Шевалле клас-
сических типов. Мы решаем аналог проблемы 1 для исключительных типов. С помощью недавно
введенной конструкции В. М. Левчука обертывающих алгебр для N (K) исключительного типа
F4 найдены обертывающие алгебры как с нестандартными иделами, так и без них
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