Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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THE MATRIX REPRESENTATION OF CLIFFORD ALGEBRA

  • Lee, Doohann (Department of Mathematics Education, Sangmyung University) ;
  • Song, Youngkwon (Department of Mathematics, Kwangwoon University)
  • Received : 2010.04.21
  • Accepted : 2010.06.01
  • Published : 2010.06.30
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Abstract

In this paper we construct a subalgebra $L_8$ of $M_8({\mathbb{R}})$ which is a generalization of the algebra of quaternions. Moreover we prove that the algebra $L_8$ is the real Clifford algebra $Cl_3$, and so $L_8$ is a matrix representation of Clifford algebra $Cl_3$.

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Acknowledgement

Supported by : Korea Research Foundation

References

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  2. Andrew Baker, Matrix Groups. An Introduction to Lie Group Theory, SUMS. Springer, 2002.
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  4. Ian Porteous, Clifford Algebras and the Classical Groups, Cambridge University Press, 1995.