충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제23권2호
  • /
  • Pages.363-368
  • /
  • 2010
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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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)
  • 투고 : 2010.04.21
  • 심사 : 2010.06.01
  • 발행 : 2010.06.30
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초록

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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과제정보

연구 과제 주관 기관 : Korea Research Foundation

참고문헌

  1. J. C. Baez, The Octonions, Bull. Amer. Math. Soc. 39 (2002), 145-205.
  2. Andrew Baker, Matrix Groups. An Introduction to Lie Group Theory, SUMS. Springer, 2002.
  3. Pertti Lounesto, Clifford Algebras and Spinors, LMSLNS No. 286, Cambridge University Press, second edition, 2001.
  4. Ian Porteous, Clifford Algebras and the Classical Groups, Cambridge University Press, 1995.