Part of the series of explicit functors giving category equivalences:
cliffordModule
cliffordModuleToCIResolution
cliffordModuleToMatrixFactorization
ciModuleToMatrixFactorization
ciModuleToCliffordModule
A Clifford module M on the Clifford algebra C:=Cliff(qq) of a quadratic form qq has keys evenOperator and oddOperator, the list of the even operators uEv_i : M_0 \to M_1 and the odd operators uOdd_i : M_1 \to M_0, which form a representation of C.
From this representation we read off a matrix factorization (M1, M2) of qq.
i1 : kk=ZZ/101; |
i2 : g=1; |
i3 : rNP=randNicePencil(kk,g); |
i4 : qq=rNP.quadraticForm; |
i5 : S=rNP.qqRing; |
i6 : cM=cliffordModule(rNP.matFact1,rNP.matFact2,rNP.baseRing) o6 = CliffordModule{...6...} o6 : CliffordModule |
i7 : (M1,M2)=cliffordModuleToMatrixFactorization(cM,S); |
i8 : r=rank source M1 o8 = 8 |
i9 : M1*M2 - qq*id_(S^r) == 0 o9 = true |
i10 : M1 == rNP.matFact1 o10 = true |
i11 : M2 == rNP.matFact2 o11 = true |
i12 : cMu=cliffordModule(rNP.matFactu1,rNP.matFactu2,rNP.baseRing) o12 = CliffordModule{...6...} o12 : CliffordModule |
i13 : (Mu1,Mu2)=cliffordModuleToMatrixFactorization(cMu,S); |
i14 : ru=rank source Mu1 o14 = 4 |
i15 : Mu1*Mu2 - qq*id_(S^ru) == 0 o15 = true |
i16 : Mu1 == rNP.matFactu1 o16 = true |
i17 : Mu2 == rNP.matFactu2 o17 = true |
The object cliffordModuleToMatrixFactorization is a method function.