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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2018, Volume 24, Number 4, Pages 135–145
DOI: https://doi.org/10.21538/0134-4889-2018-24-4-135-145
(Mi timm1581)
 

This article is cited in 1 scientific paper (total in 1 paper)

The Mal'tsev correspondence and isomorphisms of niltriangular subrings of Chevalley algebras

I. N. Zotov, V. M. Levchuk

Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk
Full-text PDF (235 kB) Citations (1)
References:
Abstract: Models of algebraic systems of a first-order language are called elementarily equivalent (we write $\equiv$) if every sentence that is true in one of the models is also true in the other model. The model-theoretic study of linear groups and rings initiated by A.I. Mal'tsev (1960, 1961) is closely related to isomorphism theory; as a rule, the relation $\equiv$ of systems was transferred to fields (or rings encountered) of the coefficients. The Mal'tsev correspondence was analyzed for rings of niltriangular matrices and unitriangular groups (B. Rose, 1978; V. Weiler, 1980; K. Videla, 1988; O.V. Belegradek, 1999; V.M. Levchuk, E.V. Minakova, 2009). For unipotent subgroups of Chevalley groups over a field $K$, the correspondence was studied in 1990 by Videla for $char~ \, K\ne 2,3$. Earlier the authors announced a weakening of the constraint on the field $K$ in the Videla theorem. In the Chevalley algebra associated with a root system $\Phi$ and a ring $K$, the niltriangular subalgebra $N\Phi(K)$ is naturally distinguished. The main results of this paper establish the Mal'tsev correspondence (related with the description of isomorphisms) for the Lie rings $N\Phi(K)$ of classical types over arbitrary associative commutative rings with unity. A corollary is noted for (nonassociative) enveloping algebras to $N\Phi(K)$.
Keywords: Chevalley algebra, niltriangular subalgebra, isomorphism, model-theoretic Mal'tsev correspondence.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00707
This work was supported by the Russian Foundation for Basic Research (project no. 16-01-00707).
Received: 10.09.2018
Revised: 20.11.2018
Accepted: 26.11.2018
Bibliographic databases:
Document Type: Article
UDC: 512.55
MSC: 17B30, 17B40, 03C07
Language: Russian
Citation: I. N. Zotov, V. M. Levchuk, “The Mal'tsev correspondence and isomorphisms of niltriangular subrings of Chevalley algebras”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 4, 2018, 135–145
Citation in format AMSBIB
\Bibitem{ZotLev18}
\by I.~N.~Zotov, V.~M.~Levchuk
\paper The Mal'tsev correspondence and isomorphisms of niltriangular subrings of Chevalley algebras
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2018
\vol 24
\issue 4
\pages 135--145
\mathnet{http://mi.mathnet.ru/timm1581}
\crossref{https://doi.org/10.21538/0134-4889-2018-24-4-135-145}
\elib{https://elibrary.ru/item.asp?id=36517705}
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  • This publication is cited in the following 1 articles:
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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