The Category Quad

  • Gabriele Nebe
  • Eric M. Rains
  • Neil J.A. Sloane
Part of the Algorithms and Computation in Mathematics book series (AACIM, volume 17)


This chapter studies the objects introduced in Chapter 1 from the point of view of category theory. One of the main reasons for doing this is so that we can introduce the notion of a matrix ring over a form ring (see §1.10), which will be used to define the hyperbolic co-unitary group (see (5.2.5)) and in the proofs of the main theorems in Chapter 5. Another application will be the definition of the Witt group of representations of a form ring (§4.6). This will be used to define the universal Clifford-Weil group associated with a finite form ring (see §5.4).


Abelian Group Quadratic Form Direct Summand Form Ring Projective Representation 
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Copyright information

© Springer 2006

Authors and Affiliations

  • Gabriele Nebe
    • 1
  • Eric M. Rains
    • 2
  • Neil J.A. Sloane
    • 3
  1. 1.Lehrstuhl D für Mathematik Rheinisch-Westfälische Technische Hochschule AachenAachenGermany
  2. 2.Department of MathematicsUniversity of California at DavisDavisUSA
  3. 3.Internet and Network Systems Research AT&T Shannon LabsFlorham ParkUSA

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