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gptkbp:instanceOf
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gptkb:algebra
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gptkbp:application
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gptkb:theoretical_physics
differential geometry
quantum mechanics
representation theory
spin geometry
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gptkbp:automorphismGroup
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gptkb:Pin_group
gptkb:Spin_group
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gptkbp:basisFor
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generated by 1 and n orthogonal elements
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gptkbp:builtBy
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real vector space with quadratic form
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gptkbp:category
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gptkb:associative_algebra
graded algebra
quadratic algebra
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gptkbp:centralTo
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depends on signature (p,q)
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gptkbp:class
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gptkb:Bott_periodicity
8-fold periodicity
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gptkbp:dimensions
|
2^n (for n-dimensional vector space)
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gptkbp:field
|
real numbers
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gptkbp:firstDefined
|
1878
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gptkbp:generalizes
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real quadratic forms
exterior algebra
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gptkbp:hasSubalgebra
|
exterior algebra
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https://www.w3.org/2000/01/rdf-schema#label
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real Clifford algebra
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gptkbp:namedAfter
|
gptkb:William_Kingdon_Clifford
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gptkbp:notation
|
Cl(V,Q) or Cl(p,q)
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gptkbp:property
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associative
unital
non-commutative (in general)
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gptkbp:relatedTo
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gptkb:Clifford_module
gptkb:algebra
gptkb:Clifford_group
gptkb:Grassmann_algebra
gptkb:Dirac_algebra
gptkb:orthogonal_groups
Pauli matrices
orthogonal transformations
geometric algebra
gamma matrices
reflection groups
spinors
spin representation
Cartan-Dieudonné theorem
Dirac spinors
Majorana spinors
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gptkbp:subclassOf
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gptkb:complex_Clifford_algebra
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gptkbp:usedIn
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gptkb:mathematics
physics
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gptkbp:bfsParent
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gptkb:Clifford_algebras
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gptkbp:bfsLayer
|
7
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