special linear group SL(n,C)

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:group_of_people gptkb:Lie_group
gptkbp:actsOn	complex n-dimensional vector space
gptkbp:centralTo	set of scalar matrices with n-th roots of unity
gptkbp:compact	true
gptkbp:consistsOf	n x n complex matrices with determinant 1
gptkbp:definedIn	complex numbers
gptkbp:determinant	1
gptkbp:dimensions	n^2-1
gptkbp:hasConnection	true
gptkbp:hasSubgroup	gptkb:general_linear_group_GL(n,C)
https://www.w3.org/2000/01/rdf-schema#label	special linear group SL(n,C)
gptkbp:isAlgebraicGroup	true
gptkbp:isClassicalGroup	true
gptkbp:isConnectedComponentOfIdentity	true
gptkbp:isNonAbelian	true
gptkbp:isReductive	true
gptkbp:isSemisimple	true
gptkbp:isSimple	n >= 2
gptkbp:Lie_algebra	gptkb:sl(n,C)
gptkbp:notation	gptkb:SL(n,C)
gptkbp:universalCover	gptkb:projective_special_linear_group_PSL(n,C)
gptkbp:usedIn	gptkb:algebraic_geometry gptkb:gauge_theory gptkb:theoretical_physics gptkb:topology gptkb:Hodge_theory gptkb:Langlands_program gptkb:algebraic_K-theory gptkb:string_theory complex analysis differential geometry dynamical systems invariant theory modular forms number theory partial differential equations quantum mechanics representation theory algebraic groups automorphic forms moduli spaces symplectic geometry complex geometry geometric representation theory monodromy representations
gptkbp:bfsParent	gptkb:unitary_group_U(n)
gptkbp:bfsLayer	6