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Advances in Applied Clifford Algebras

, Volume 7, Issue 2, pp 103–111 | Cite as

Spin invariants of multivectors

  • J. G. Maks
Papers
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Abstract

LetCl(p, q) be a real universal Clifford algebra which is isomorphic to a full matrix algebra ℝ(2m).

In this paper we show that on the linear subspaceClk(p, q) ofk-vectors the determinant can be written as a product of two polynomialsdi of degreem and that on the subset ofdecomposable k-vectors we have det=±Qm for some quadratic formQ.

The polynomialsdi andQ are examples of a spin invariant, the latter being defined as a functionJ:Cl k (p,q) → ℝ for whichJ(sus−1)=J(u) for alluClk(p, q) andsSpin(p, q).

In the last section we identify the ‘fundamental’ spin invariants on the bivector spacesCl2(p, p) forp=2 andp=3.

Keywords

Quadratic Form Clifford Algebra Matrix Algebra Determinant Function Apply Clifford Algebra 
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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References

  1. [1]
    Ablamowicz R., P. Lounesto, J. Maks, Conference Report, Second Workshop on Clifford Algebras and Their Applications in Mathematical Physics, Montpellier, France, 1989,Found. Phys. 21, No. 6, 1991.Google Scholar
  2. [2]
    Porteous I. R., Clifford algebras and the classical groups, Cambridge University Press, 1995.Google Scholar

Copyright information

© Birkhäuser-Verlag AG 1997

Authors and Affiliations

  1. 1.Department of MathematicsDelft University of TechnologyGA DelftThe Netherlands

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