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.
Research supported by National Science Foundation grant #MC879-04473, at Yale University. The author expresses his thanks as well to the Institute des Hautes Etudes Scientifiques for its generous hospitality.
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Seligman, G.B. (1983). Higher even clifford algebras. In: Malliavin, MP. (eds) Séminaire d’Algèbre Paul Dubreil et Marie-Paule Malliavin. Lecture Notes in Mathematics, vol 1029. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098931
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DOI: https://doi.org/10.1007/BFb0098931
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