# 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:

- 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}

}

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