DOI QR코드

DOI QR Code

VECTOR GENERATORS OF THE REAL CLIFFORD ALGEBRA Cℓ0,n

  • Received : 2014.07.09
  • Accepted : 2014.10.06
  • Published : 2014.11.15

Abstract

In this paper, we present new vector generators of a matrix subalgebra $L_{0,n}$, which is isomorphic to the Clifford algebra $C{\ell}_{0,n}$, and we obtain the matrix form of inverse of a vector in $L_{0,n}$. Moreover, we consider the solution of a linear equation $xg_2=g_2x$, where $g_2$ is a vector generator of $L_{0,n}$.

Keywords

References

  1. J. Gallier, Clifford Algebras, Clifford Groups, and a Generation of the Quater- nions: The Pin and Spin Groups, Preprint (2002)
  2. D. Lee and Y. Song, Explicit Matrix Realization of Clifford Algebras, Adv. Appl. Clifford Algebras 23 (2013), 441-451 https://doi.org/10.1007/s00006-013-0382-8
  3. Y. Song and D. Lee, Matrix Representations of the Low Order Real Clifford Algebras, Adv. Appl. Clifford Algebras 23 (2013), 965-980. https://doi.org/10.1007/s00006-013-0407-3
  4. C. P. Poole, Jr., H. A. Farach, Pauli-Dirac matrix generators of Clifford algebras, Found. of Phys. 12 (1982), 719-738. https://doi.org/10.1007/BF00729808
  5. Y. Tian, Universal similarity factorization equalities over real Clifford algebras, Adv. Appl. Clifford Algebras 8 (1998), 365-402. https://doi.org/10.1007/BF03043105