Endlichdimensionale graduierte Algebren und ihre Darstellungen. (Finite- dimensional graded algebras and their representations) (Q1101527)

The authors prove some elementary results concerning complex finite- dimensional associative graded algebras H and their irreducible (graded) representations. For any abelian group A of degrees, they characterize the A-gradation of H in terms of a homomorphism of the character group \(A^*\) of A into the automorphism group Aut(H) of H. For \(A={\mathbb{Z}}_ 2\) (the ``super'' case), they establish a canonical relationship between the irreducible representations (in the usual non-graded sense) and the graded irreducible representations of H. The case of the Clifford algebras serves to exemplify the results.