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JOURNALS // Matematicheskii Sbornik // Archive

Mat. Sb., 1997 Volume 188, Number 9, Pages 55–82 (Mi sm257)

This article is cited in 3 papers

Maximal tori of a general Lie algebra of Cartan type

M. I. Kuznetsov

N. I. Lobachevski State University of Nizhni Novgorod

Abstract: A description is given of all maximal tori in the $p$-closure of a general Lie algebra $W(\mathscr F)$ of Cartan type over an algebraically closed field of characteristics of tori are found (dimension, algebra of invariants, weight functions root subspaces, the centralizer of a maximal torus) in terms of a defining system of functions of a maximal torus, and criteria are obtained for standartness and optimality of a maximal torus. A connection is established between the maximal tori in the $p$-closure and the Cartan subalgebras of $W(\mathscr F)$.

UDC: 512.554.31

MSC: Primary 17B50; Secondary 17B10, 17B40, 17B56, 17B20, 17B05

Received: 14.01.1997

DOI: 10.4213/sm257


 English version:
Sbornik: Mathematics, 1997, 188:9, 1317–1342

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