Geodesic
Maximal abelian ideals and automorphisms of nonfinitary nil-triangular algebras
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 635-640.

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We study mutually connected automorphisms and abelian ideals of nonfinitary nil-triangular algebras.
Keywords: Chevalley algebra, unitriangular group, finitary and nonfinitary generalizations, automorphisms, abelian ideal.
Mots-clés : nil-triangular subalgebra 
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Elena A. Sotnikova. Maximal abelian ideals and automorphisms of nonfinitary nil-triangular algebras. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 635-640. http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a9/

[1] J.V. Bekker, V.M. Levchuk, E.A. Sotnikova, “Nonfinitary generalizations of nil-triangular subalgebras of Chevalley algebras”, Bulletin of Irkutsk state university, Series mathematics, 29 (2019), 39–51 (in Russian) | DOI | MR | Zbl

[2] J.V. Bekker, D.V. Levchuk, E.A. Sotnikova, “Automorphisms of rings of nonfinitary niltriangular matrices”, Trudy Instituta Matematiki i Mekhaniki URO RAN, 26, no. 3, 2020, 7–13 (in Russian) | DOI | MR

[3] I.N. Zotov, V.M. Levchuk, “Nonfinitary algebras and their automorphism groups”, Siberian Mathematical Journal, 63:1 (2022), 87–96 | DOI | MR | Zbl

[4] R. Carter, Simple Groups of Lie type, Wiley and Sons, New York, 1972 | MR | Zbl

[5] V.M. Levchuk, “Automorphisms of unipotent subgroups of Chevalley groups”, Algebra and Logic, 29:3 (1990), 211–224 | DOI | MR | Zbl

[6] R. Slowik, “Bijective maps of infinite triangular and unitriangular matrices preserving commutators”, Linear and Multilinear Algebra, 61:8 (2013), 1028–1040 | DOI | MR | Zbl

[7] E.A. Sotnikova, “Nonfinitary generalizations of nil-triangular subalgebras of Chevalley algebras”, International conference (Krasnoyarsk, SFU, 2019), 1075–1077 (in Russian)

[8] V.M. Levchuk, “Some locally nilpotent rings and their associated groups”, Math Notes, 42:5 (1987), 631–641 | DOI | MR | Zbl

[9] F. Kuzucuoglu, V.M. Levchuk, “Isomorphisms of Certain Locally Nilpotent Finitary Groups and Associated Rings”, Acta Applicandae Mathematicae, 82:2 (2004), 169–181 | DOI | MR | Zbl

[10] V.M. Levchuk, A.V. Litavrin, “Hypercentral automorphisms of nil-triangular subalgebras in Chevalley algebras”, Sib. Elektron. Mat. Izv., 13 (2016), 467–477 (in Russian) | DOI | MR | Zbl

[11] V.M. Levchuk, “Connections between a unitriangular group and certain rings. Chap. 2: Groups of automorphisms”, Siberian Mathematical Journal, 24:4 (1983), 543–557 | DOI | MR | Zbl