Projective Points Over Matrices and Their Separability Properties

Autor: Alfonso F. Agnew, Matt Rathbun, William Terry
Rok vydání: 2022
Předmět:
Zdroj: Advances in Applied Clifford Algebras. 32
ISSN: 1661-4909
0188-7009
DOI: 10.1007/s00006-022-01212-4
Popis: In this article we consider topological quotients of real and complex matrices by various subgroups and their connections to spacetime structures. These spaces are naturally interpreted as projective points. In particular, we look at quotients of nonzero matrices $$M^*_2({\mathbb {F}})$$ M 2 ∗ ( F ) by $$GL_2({\mathbb {F}}),$$ G L 2 ( F ) , $$SL_2({\mathbb {F}}),$$ S L 2 ( F ) , $$O_2({\mathbb {F}}),$$ O 2 ( F ) , and $$SO_2({\mathbb {F}})$$ S O 2 ( F ) and prove various results about their topological separability properties. We discuss the interesting result that, as the group we quotient by gets smaller, the separability properties of the quotient improve.
Databáze: OpenAIRE
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