Co.Al.A.R.
Computational Algebraic Analysis Results
 

THIS PAGE IS DEVOTED TO SOME RESULTS IN CLIFFORD ANALYSIS and related topics


last update: 01 Feb 2006

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==> BIREGULAR FUNCTIONS [DSS1]:
 
Graded Betti gd(l)numbers for the resolution associated to 2n operators (n left and n right Cauchy-Fueter), n>2.
 If i-th free R-module in the resolution is denoted with

... --> Ål R(-l)gd(l) --> ...
 

then the d-th Betti number in degree l can be expressed as in the following table. Note that for d<=2n+1 there is no compact form for the graded Betti numbers. We have then just indicated the ones up to d=3.

d

 l gd(l)
0 0 4
1 1 8n
2 2 4n2
2 3 16*(n choose 2) + 32*(n choose 3)
3 4 (4/9)* n2 *(2n-1 choose 2)2
... ... ...
d > 2n+1 d+2 4n2Σ{s+t=d+2} (2n-1 choose s-1)*(2n-1 choose t-1)*(1- (2d/st))
 
 
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[DSS1] A. Damiano, I. Sabadini, D. Struppa, New Algebraic Properties of Biregular Functions in $2n$ Quaternionic Variables. Submitted 2004.