Non-finitary Generalizations of Nil-triangular Subalgebras of Chevalley Algebras : научное издание

Описание

Тип публикации: статья из журнала

Год издания: 2019

Идентификатор DOI: 10.26516/1997-7670.2019.29.39

Ключевые слова: Chevalley algebra, nil-triangular subalgebra, unitriangular group, finitary and nonfinitary generalizations, radical ring

Аннотация: Let N Phi(K) be a niltriangular subalgebra of Chevalley algebra over a field or ring K associated with root system (13 of classical type. For type A(n-1) it is associated to algebra NT (n, K) of (lower) nil -triangular n x n- matrices over K. The algebra Let N Phi(K) be a niltriangular subalgebra of Chevalley algebra over a field Показать полностьюor ring K associated with root system (13 of classical type. For type A(n-1) it is associated to algebra NT (n, K) of (lower) nil -triangular n x n- matrices over K. The algebra Let NΦ(K) be a niltriangular subalgebra of Chevalley algebra over a field or ring K associated with root system Φ of classical type. For type An−1 it is associated to algebra NT (n, K) of (lower) nil-triangular n × n- matrices over K. The algebra R = NT (Γ, K) of all nil-triangular Γ-matrices α = ||aij||i,jεΓ over K with indices from chain Γ of natural numbers gives its non-finitary generalization. It is proved, (together with radicalness of ring R) that if K is a ring without zero divizors, then ideals Ti,i-1 of all Γ-matrices with zeros above i-th row and in columns with numbers ≥ i exhausts all maximal commutative ideals of the ring R and associated Lie rings R(-), and also maximal normal subgroups of adjoint group (it is isomorphic to the generalize unitriangular group UT (Γ, K)). As corollary we obtain that the automorphism groups Aut R and Aut R(-) coincide. Partially automorphisms studied earlier, in particulary, for Aut UT (Γ, K) when K is a field. Well-known (1990) special matrix representation of Lie algebras NΦ(K) allows to construct non-finitary generalizations NG(K) of type G = BΓ, CΓ and DΓ. Be research automorphisms by transfer to factors of Lie ring NG(K) which is isomorphic to NT (Γ, K). On the other hand, for any chain Γ finitary nil-triangular Γ-matrices forms finitary Lie algebra F NG(Γ, K) of type G = AΓ (i.e., F NG(Γ, K)), BΓ, CΓ and DΓ. Earlier automorphisms was studied (V. M. Levchuk and G. S. Sulejmanova, 1987 and 2009) for Lie ring F NT (Γ, K) over ring K without zero divizors and, also, for finitary generalizations of unipotent subgroups of Chevalley group of classical type over the field (including twisted types). © 2019 Irkutsk State University. All rights reserved.

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Издание

Журнал: BULLETIN OF IRKUTSK STATE UNIVERSITY-SERIES MATHEMATICS

Выпуск журнала: Vol. 29

Номера страниц: 39-51

ISSN журнала: 19977670

Место издания: IRKUTSK

Издатель: IRKUTSK STATE UNIV

Авторы

  • Bekker J.V. (Siberian Fed Univ, 79 Svobodniy Ave, Krasnoyarsk 660041, Russia)
  • Levchuk V.M. (Siberian Fed Univ, 79 Svobodniy Ave, Krasnoyarsk 660041, Russia; Siberian Fed Univ, Sci Phys & Math, 79 Svobodniy Ave, Krasnoyarsk 660041, RussiaArticle)
  • Sotnikova E.A. (Siberian Fed Univ, 79 Svobodniy Ave, Krasnoyarsk 660041, Russia)

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