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Title: Examples of explicit calculation of the inductive limit of a family of Lie algebras

Abstract

The inductive limits of some families of Lie algebras are considered. Under discussion are algebras of vector fields on a manifold that preserve a volume form or a symplectic form and have supports in coordinate neighbourhoods. The family of all commutative subalgebras of the Lie algebra of the skew-Hermitian matrices of order larger than two is studied. The explicit form of the inductive limits is indicated.

Authors:
 [1]
  1. N.E. Bauman Moscow State Technical University, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
21202916
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 191; Journal Issue: 3; Other Information: DOI: 10.1070/SM2000v191n03ABEH000463; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; COORDINATES; HERMITIAN MATRIX; LIE GROUPS; VECTOR FIELDS

Citation Formats

Ismagilov, R S. Examples of explicit calculation of the inductive limit of a family of Lie algebras. United States: N. p., 2000. Web. doi:10.1070/SM2000V191N03ABEH000463; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Ismagilov, R S. Examples of explicit calculation of the inductive limit of a family of Lie algebras. United States. doi:10.1070/SM2000V191N03ABEH000463; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Ismagilov, R S. Sun . "Examples of explicit calculation of the inductive limit of a family of Lie algebras". United States. doi:10.1070/SM2000V191N03ABEH000463; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21202916,
title = {Examples of explicit calculation of the inductive limit of a family of Lie algebras},
author = {Ismagilov, R S},
abstractNote = {The inductive limits of some families of Lie algebras are considered. Under discussion are algebras of vector fields on a manifold that preserve a volume form or a symplectic form and have supports in coordinate neighbourhoods. The family of all commutative subalgebras of the Lie algebra of the skew-Hermitian matrices of order larger than two is studied. The explicit form of the inductive limits is indicated.},
doi = {10.1070/SM2000V191N03ABEH000463; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 3,
volume = 191,
place = {United States},
year = {2000},
month = {4}
}