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Cycles in the Chamber Homology for SL (2, F)

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2014

Key Words:

Author Name
Abstract (2. Language): 
We emphasized finding the explicit cycles in the chamber homology groups and the K-theory groups in term of each representation for SL(2,F). This led to an explicit computing of chamber homology and the K-theory groups. We have identified the base change effect on each of these cycles. The base change map on the homology group level works by sending a generator of the homology group of SL(2, E) labeled by a character of E * to the generator of the homology group of SL(2, F) labeled by a character of F* multiplied by the residue field degree. Whilst, it works by sending the K-theory group generator of the reduce C*-algebra of SL(2,E) labeled by the 1-cycle (resp. 0-cycle) to the multiplication of the residue field degree with a generator of the K-theory group of SL(2,F) labeled by the base changed effect on 1-cycle (resp. 0-cycle).
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REFERENCES

References: 

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