Topological uniqueness results for the special linear and other classical Lie Algebras.

Suppose L is a complete separable metric topological group (ring, field, etc.). L is topologically unique if the Polish topology on L is uniquely determined by its underlying algebraic structure. More specifically, L is topologically unique if an algebraic isomorphism of L with any other complete separable metric topological group (ring, field, etc.) induces a topological isomorphism. A local field is a locally compact topological field with non-discrete topology. The only local fields (up to isomorphism) are the real, complex, and p-adic numbers, finite extensions of the p-adic numbers, and fields of formal power series over finite fields. We establish the topological uniqueness of the special linear Lie algebras over local fields other than the complex numbers (for which this result is not true) in the context of complete separable metric Lie rings. Along the way the topological uniqueness of all local fields other than the field of complex numbers is established, which is derived as a corollary to more general principles which can be applied to a larger class of topological fields. Lastly, also in the context of complete separable metric Lie rings, the topological uniqueness of the special linear Lie algebra over the real division algebra of quaternions, the special orthogonal Lie algebras, and the special unitary Lie algebras is proved.

Grantor dc:publisher

University of North Texas

Year dc:date

2001

Author dc:creator

• Rees, Michael K.

Contributors dc:contributor

• Kallman, Robert
• Brand, Neal

• Lie algebras.
• Algebras, Linear.
• Topological algebras.
• Polish spaces (Mathematics)
• complex numbers
• Lie algebra
• local field
• topological uniqueness
• polish space

Statement dc:rights

• Use restricted to UNT Community
• Copyright
• Rees, Michael K.
• Copyright is held by the author, unless otherwise noted. All rights reserved.

Language dc:language

English

Identifier

oclc: 51959465
https://digital.library.unt.edu/ark:/67531/metadc3000/
ark: ark:/67531/metadc3000

OAI identifier oai:identifier

info:ark/67531/metadc3000