symplectic group Sp(2g, Z)

URI: https://gptkb.org/entity/symplectic_group_Sp(2g,_Z)
GPTKB entity
Statements (28)
Predicate Object
gptkbp:instanceOf gptkb:group_of_people
gptkb:orthogonal_group
gptkbp:actsOn 2g-dimensional integer lattice
gptkbp:centralTo {±I} for g > 1
gptkbp:definedIn integers
gptkbp:firstHomologyGroupOf mapping class group of genus g surface
gptkbp:generation elementary symplectic matrices
gptkbp:hasCongruenceSubgroups true
gptkbp:hasSubgroup general linear group GL(2g, Z)
gptkbp:isAlgebraicGroup true
gptkbp:isDiscreteSubgroupOf symplectic group Sp(2g, R)
gptkbp:isFinitelyGenerated true
gptkbp:isMatrixGroup true
gptkbp:isPerfect for g > 2
gptkbp:isQuotientOf projective symplectic group PSp(2g, Z)
gptkbp:isResiduallyFinite true
gptkbp:notation Sp(2g, Z)
gptkbp:order infinite
gptkbp:originatedIn gptkb:algebraic_geometry
gptkb:topology
number theory
moduli theory
gptkbp:preserves symplectic form
gptkbp:relatedTo gptkb:mapping_class_group
gptkb:modular_group
gptkbp:bfsParent gptkb:Siegel_modular_variety
gptkbp:bfsLayer 8
https://www.w3.org/2000/01/rdf-schema#label symplectic group Sp(2g, Z)