Higher even clifford algebras

  • George B. Seligman
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1029)


Associated with a nondegenerate hermitian or antithermitian form on a finite-dimensional vector space V over an involutorial division algebra D of finite dimension over its center (of characteristic zero), we define by generators and relations an infinite sequence of finite-dimensional semisimple associative algebras. The representation theory of all these algebras, taken together, is essentially that of the Lie algebra of skew D-endomorphisms of V. The case where D is commutative is presented in detail here; when the form is symetric, the first non-trivial algebra in the sequence is the even Clifford algebra.


High Weight Clifford Algebra Irreducible Module Central Simple Algebra Symplectic Space 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • George B. Seligman
    • 1
  1. 1.Yale UniversityNew Haven

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