analytic groups

[/ˌænəˈlɪtɪk ɡruːps/]
nounpl: analytic groups
grupos analíticos
1. In mathematics, groups that have the structure of analytic manifolds, where the group operations (multiplication and inversion) are analytic functions
Analytic groups are fundamental objects in the study of Lie groups and differential geometry.
Os grupos analíticos são objetos fundamentais no estudo de grupos de Lie e geometria diferencial.
2. Groups whose elements can be studied using methods from complex or real analysis
The properties of analytic groups can be investigated through their analytic functions.
As propriedades dos grupos analíticos podem ser investigadas através de suas funções analíticas.
This is specialized mathematical terminology primarily used in academic and research contexts. It appears in university courses on advanced mathematics, particularly in differential geometry and algebraic topology programs. The term is used identically across Portuguese-speaking and English-speaking mathematical communities, as mathematical terminology is largely internationalized.
Synonyms / Sinônimos
Lie groupssmooth groupsdifferentiable groups
Antonyms / Antônimos
discrete groupsfinite groups

Regional Variations

General Brazilian
grupos analíticos
Standard mathematical terminology used in Brazilian universities and research
Portugal
grupos analíticos
Same terminology used in Portuguese academic institutions
USA/International
analytic groups
Standard English mathematical terminology in academic contexts

Related Words

manifoldLie algebradifferential geometrygroup theoryholomorphic functions
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