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Higher even clifford algebras

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

Abstract

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.

Keywords

High Weight Clifford Algebra Irreducible Module Central Simple Algebra Symplectic Space 
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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Bibliography

  1. [1]
    Bourbaki, N., Groupes et algèbres de Lie, chaps. IV–VI. Eléments de Mathématiques, Fasc. XXXIV. Hermann, Paris, 1968.zbMATHGoogle Scholar
  2. [2]
    Cartan, E., Leçons sur la théorie des spineurs, vol. II. Hermann, Paris, 1938. English translation, the theory of spinors, M.I.T. Press, Cambridge(MA), 1967.Google Scholar
  3. [3]
    Chevalley, C., The algebraic theory of spinors. Columbia University Press, New York, 1954.zbMATHGoogle Scholar
  4. [4]
    Jacobson, N., Basic algebra II. Freeman, San Fransisco, 1980.zbMATHGoogle Scholar
  5. [5]
    _____, Lie algebras. Interscience, New York, 1962. Republished Dover, New York, 1979.zbMATHGoogle Scholar
  6. [6]
    _____, Structure and representations of Jordan algebras, Amer. Math. Soc. Colloq. Publs. Vol. XXXIX. A.M.S., Providence, 1968.zbMATHCrossRefGoogle Scholar
  7. [7]
    O’Meara, O. T., Introduction to quadratic forms. Academic press-Springer, New York, 1963.zbMATHCrossRefGoogle Scholar
  8. [8]
    Seligman, G.B., Rational constructions of modules for simple Lie algebras, Contemp. Math., Vol. 5, A.M.S., Providence, 1981.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

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

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