p-adic analytic groups
E581256
p-adic analytic groups are topological groups over the p-adic numbers that locally resemble finite-dimensional p-adic manifolds and admit a compatible analytic structure.
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
p-adic Lie group ⓘ topological group theory concept ⓘ |
| admits | p-adic Lie algebra ⓘ |
| associatedWith | p-adic differential equations ⓘ |
| compatibilityCondition | group operations are analytic maps ⓘ |
| contrastWith |
complex Lie groups
ⓘ
real Lie groups ⓘ |
| definedOver |
Q_p
ⓘ
p-adic numbers ⓘ |
| dimension | finite ⓘ |
| field |
algebra
ⓘ
number theory ⓘ p-adic analysis ⓘ representation theory ⓘ |
| generalizes | analytic Lie groups over Q_p ⓘ |
| hasExample |
GL_n(Q_p)
NERFINISHED
ⓘ
SL_n(Q_p) NERFINISHED ⓘ Z_p^n as an additive group ⓘ compact open subgroups of GL_n(Q_p) ⓘ p-adic points of a linear algebraic group over Q_p ⓘ |
| hasInvariantMeasure | Haar measure ⓘ |
| hasMorphisms | continuous analytic group homomorphisms ⓘ |
| hasNeighborhoodBase | p-adic analytic submanifolds ⓘ |
| hasOperation |
group inversion
ⓘ
group multiplication ⓘ |
| hasProperty |
Hausdorff
NERFINISHED
ⓘ
analytic in the p-adic sense ⓘ first countable ⓘ locally compact ⓘ locally homeomorphic to Q_p^n ⓘ paracompact ⓘ totally disconnected ⓘ |
| hasStructure |
analytic structure
ⓘ
p-adic manifold ⓘ topological group ⓘ |
| hasTangentObject | Lie algebra over Q_p ⓘ |
| localCoordinateModel | open subsets of Q_p^n ⓘ |
| locallyResembles | finite-dimensional p-adic manifold ⓘ |
| relatedConcept |
Lie group
NERFINISHED
ⓘ
p-adic Lie algebra ⓘ profinite group ⓘ rigid analytic space ⓘ |
| specialCaseOf | locally analytic groups over non-Archimedean fields ⓘ |
| studiedIn |
Iwasawa theory
NERFINISHED
ⓘ
p-adic representation theory ⓘ |
| typicalTopology | non-Archimedean ⓘ |
| usedIn |
automorphic forms
ⓘ
local Langlands correspondence NERFINISHED ⓘ non-Archimedean harmonic analysis ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.