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In mathematics, the classical groups are defined as the special linear groups over the reals R, the complex numbers C and the quaternions H together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the complex classical Lie groups are four infinite families of Lie groups that together with the exceptional groups exhaust the classification of simple Lie groups. The compact classical groups are compact real forms of the complex classical groups. The finite analogues of the classical groups are the classical groups of Lie type. The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph The Cl

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rdf:type	yago:WikicatLieGroups yago:Abstraction100002137 yago:Group100031264
rdfs:label	Classical group (en) Grup clàssic (ca) Grupo clásico (es) Groupe classique (fr) 고전군 (ko) Klassieke groep (nl) 典型群 (zh)
rdfs:comment	En matemàtiques, els grups clàssics es defineixen com els grups lineals especials sobre els reals R, els complexos C i els quaternions H, juntament amb automorfismes de grups especials de formes bilineals simètriques o antisimètriques i de hermítiques o definides sobre espais vectorials de dimensió finita reals, complexos o quaterniònics. D'aquests, els grups de Lie clàssics complexos són quatre famílies infinites de grups de Lie que, juntament amb els , formen la totalitat dels . Els grups clàssics compactes són dels grups clàssics complexos. Els anàlegs finits dels grups clàssics són els clàssics. El terme grup clàssic fou creat per Hermann Weyl, a la seva monografia de 1939 . (ca) 리 군론에서, 고전군(古典群, 영어: classical group)은 실수, 복소수, 또는 사원수 계수의, 특별한 쌍선형 형식 또는 에르미트 형식을 보존하는 정사각 행렬로 구성되는 리 군이다. 이들은 모두 (중심에 대한 몫을 취하면) 단순 리 군을 이룬다. 고전군이 아닌 단순 리 군은 F₄, G₂, E₆, E₇, E₈ 밖에 없다. (ko) 在数学中，典型群（classical group）指与欧几里得空间的对称密切相关的四族无穷多李群。术语“经典”的使用取决于语境，有一定的灵活性。这个用法可能源于赫尔曼·外尔，他的专著 ) 以“典型群”为题。在菲利克斯·克莱因爱尔兰根纲领的观点下，也许反映了它们和“经典”几何（classical geometry）的关系。有时在紧群的限制下讨论典型群，这样容易处理它们的表示论和代数拓扑。但是这把一般线性群排除在外，当前都认为一般线性群是最典型的群。和典型李群相对的是，具有一样的抽象性质，但不属于同一类。 (zh) In mathematics, the classical groups are defined as the special linear groups over the reals R, the complex numbers C and the quaternions H together with special automorphism groups of symmetric or skew-symmetric bilinear forms and Hermitian or skew-Hermitian sesquilinear forms defined on real, complex and quaternionic finite-dimensional vector spaces. Of these, the complex classical Lie groups are four infinite families of Lie groups that together with the exceptional groups exhaust the classification of simple Lie groups. The compact classical groups are compact real forms of the complex classical groups. The finite analogues of the classical groups are the classical groups of Lie type. The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph The Cl (en) En mathématiques, les groupes classiques sont différentes familles de groupes de transformations liées à l'algèbre linéaire, principalement les groupes linéaires, orthogonaux, symplectiques et unitaires. Ces groupes peuvent aussi être présentés comme groupes de matrices inversibles, et des quotients de ceux-ci. Les groupes matrices carrées d'ordre n (GL(n, R)), GL(n, C)), le groupe des matrices orthogonales d'ordre n (O(n)) et le groupe des matrices unitaires d'ordre n (U(n)) sont des exemples explicites de groupes classiques. Dans ce qui suit, les corps ne sont pas supposés être commutatifs. (fr) In de groepentheorie, een deelgebied van de wiskunde, zijn de klassieke groepen de lineaire groepen over de reële getallen, de complexe getallen en de quaternionen, samen met speciale automorfismegroepen van symmetrische of antisymmetrische bilineaire vormen of sesquilineaire vormen op eindigdimensonale vectorruimten over de reële getallen, de complexe getallen en de quaternionen. (nl)
foaf:depiction
dcterms:subject	Lie groups
Wikipage page ID	10172878 (xsd:integer)
Wikipage revision ID	1122465070 (xsd:integer)
Link from a Wikipage to another Wikipage	Power series Princeton University Press Projective general linear group Projective special linear group Projective special orthogonal group Quantum mechanics Quaternion Projective unitary group Non-degenerate Bilinear form Determinant Vector space Indefinite orthogonal group Lie group Sylvester's law of inertia Compact real form Complex number Complex numbers Complexification Mathematics SO(n) SU(n) General linear group Emil Artin Lie algebra Lorentz group Élie Cartan Pin group Projective orthogonal group Projective special unitary group Spin group Symplectic group Maximal compact subgroup Automorphism Wilhelm Killing Algebraic groups Lie groups Euclidean space Field (mathematics) Finite field Dieudonné determinant Quantum chromodynamics Hamiltonian mechanics Hermann Weyl Internet Archive The Classical Groups Matrix group Simple Lie group Division ring Associative algebra Automorphism group Sp(n) Spacetime Special orthogonal group Special relativity Special unitary group Classification of finite simple groups Exceptional Lie groups Groups of Lie type Orthogonal group Real number General orthogonal group Root system Special linear group Unitary group Exponential map (Lie theory) Sesquilinear form Module (algebra) Vladimir L. Popov Springer-Verlag Rotation group Skew symmetric form Projective symplectic group Real form General symplectic group Semi-bilinear form Spinor norm
Link from a Wikipage to an external page	https://archive.org/details/geometricalgebra033556mbp/page/n115/mode/2up%3Fview=theater https://books.google.com/books%3Fid=AfYZAQAAIAAJ

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