Simple and prime graded Jordan algebras
By a theorem of \textit{O. Mathieu} [Invent. Math. 108, 455-519 (1992; Zbl 0769.17018)] it is known that the infinite dimensional simple graded Lie algebras of finite growth are either loop algebras, algebras of Cartan type or the Virasoro algebra. The paper under review deals with the same problem for Jordan algebras. The graded simple infinite dimensional Jordan algebras of finite growth (over an algebraically closed field of characteristic 0) are shown to be either loop algebras or Jordan algebras of a symmetric bilinear form. Moreover, the graded prime and nondegenerate Jordan algebras with the more restrictive condition of being of growth 1 (that is, the dimension of the homogeneous components is bounded) are proved to be either graded simple or related to loop algebras in a specific way.
infinite dimensional Jordan algebras of finite growth
scientific article; zbMATH DE number 1066139