Higher even clifford algebras
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.
KeywordsHigh Weight Clifford Algebra Irreducible Module Central Simple Algebra Symplectic Space
Unable to display preview. Download preview PDF.
- 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