Automorphisms of rings of nonfinitary niltriangular matrices [АВТОМОРФИЗМЫ КОЛЕЦ НЕФИНИТАРНЫХ НИЛЬТРЕУГОЛЬНЫХ МАТРИЦ]

Описание

Тип публикации: статья из журнала

Год издания: 2020

Идентификатор DOI: 10.21538/0134-4889-2020-26-3-7-13

Ключевые слова: automorphism, chevalley algebra, niltriangular subalgebra, nonfinitary generalizations, radical ring, unitriangular group

Аннотация: Let K be an associative ring with identity, and let Γ be an arbitrary linearly ordered set (briefly, chain). Matrices α = kaij k over K with indices i and j from Γ with respect to linear operations always form a K - module M (Γ, K). The matrix multiplication in M (Γ, K) is generally not defined if Γ is an infinite chain. The finitaПоказать полностьюry matrices in M (Γ, K) form a known ring with matrix multiplication and addition. On the other hand, as proved in 2019, for the chain Γ = N of natural numbers, the submodule in M (Γ, K) of all (lower) niltriangular matrices with matrix multiplication and addition gives a radical ring N T (Γ, K). Its adjoint group is isomorphic to the limit unitriangular group. The automorphisms of the group U T (∞, K) over a field K of order greater than 2 were studied by R. Slowik. In the present paper, it is proved that any infinite chain Γ is isometric or anti-isometric to the chain N or the chain of all integers if N T (Γ, K) with matrix multiplication is a ring. When the ring of coefficients K has no divisors of zero, the main theorem shows that the automorphisms of N T (N, K) and of the associated Lie ring, as well as of the adjoint group, are standard. © 2020 Sverre Raffnsoe. All rights reserved.

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Издание

Журнал: Trudy Instituta Matematiki i Mekhaniki UrO RAN

Выпуск журнала: Vol. 26, Is. 3

Номера страниц: 7-13

ISSN журнала: 01344889

Издатель: Krasovskii Institute of Mathematics and Mechanics

Авторы

  • Bekker Yu.V. (Siberian Federal University, Krasnoyarsk, 660041, Russian Federation)
  • Levchuk D.V. (Siberian Federal University, Krasnoyarsk, 660041, Russian Federation)
  • Sotnikova E.A. (Siberian Federal University, Krasnoyarsk, 660041, Russian Federation)