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The Category Quad

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

Abstract

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).

Keywords

Abelian Group Quadratic Form Direct Summand Form Ring Projective Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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