CLIFFORD ALGEBRAS
Acknowledgements
Introduction
Clifford Algebras
Print Names for Generators
Elements of a Clifford Algebra
The Main Involutions
Clifford Algebra Structure
Vector and Spin Representations
The Clifford Group
Siegel Transformations and Spin Groups
Spin Representations
Bibliography
Introduction
Clifford Algebras
CliffordAlgebra(Q) : AlgMatElt -> AlgClff, ModTupFld, Map
CliffordAlgebra(V) : ModTupFld -> AlgClff, Map
Example AlgClff_CliffQuatEx (H97E1)
Print Names for Generators
AssignNames(~C, S) : AlgClff, [ MonStgElt ]) ->
Name(C, i) : AlgClff, RngIntElt -> AlgClffElt
AsPolynomial(v) : AlgClffElt ->
Example AlgClff_CliffordGen (H97E2)
Example AlgClff_CliffordNames (H97E3)
Elements of a Clifford Algebra
elt< C | r1, r2, ..., rm > : AlgClff, RngElt, RngElt, ..., RngElt -> AlgClffElt
C ! L : AlgClff, SeqEnum[RngElt] -> AlgGenElt
SeqToClifford(C, ss) : AlgClff, SeqEnum -> AlgClffElt
SeqFromClifford(v) : AlgClffElt -> SeqEnum
Example AlgClff_Eltfromseq (H97E4)
BasisProduct(C, i, j) : AlgClff, RngIntElt, RngIntElt -> AlgGenElt
BasisProduct(C, L) : AlgClff, SeqEnum -> AlgGenElt
BasisElement(C, S) : AlgClff, SetEnum -> AlgClffElt
The Main Involutions
MainInvolution(C) : AlgClff -> Map
MainAntiautomorphism(C) : AlgClff -> Map
Clifford Algebra Structure
HomogeneousComponent(v,k) : AlgClffElt, RngIntElt -> AlgClffElt
Example AlgClff_HomComp (H97E5)
EvenSubalgebra(C : parameters) : AlgClff -> AlgAss, Map
Example AlgClff_CliffGenQuatEx (H97E6)
Centre(C) : AlgClff -> AlgAss, Map
Example AlgClff_EvenDimPlus (H97E7)
Example AlgClff_EvenDimMinus (H97E8)
Example AlgClff_OddDim (H97E9)
Vector and Spin Representations
The Clifford Group
VectorAction(g) : AlgClffElt -> AlgMatElt
Example AlgClff_ClffRef (H97E10)
Siegel Transformations and Spin Groups
Example AlgClff_siegel (H97E11)
Example AlgClff_vecrep (H97E12)
Spin Representations
ActionMatrix(S, s) : AlgAss, AlgAssElt -> AlgMatElt
Example AlgClff_ideals (H97E13)
Example AlgClff_spinrep (H97E14)
Bibliography
[Next][Prev] [Right] [____] [Up] [Index] [Root]
|