On regular Bernstein algebras
Given a Bernstein algebra which is regular (that is, \(AV=0\), where \(V\) is the null Peirce space relative to any idempotent) and nuclear (\(A^2=A\)), and once an idempotent is fixed, the algebra is determined by an onto linear map \(S^2(U)\to V\), where \(U\) is the one-half Peirce component and \(S^2(U)\) the space of symmetric tensors on \(U\) of degree 2. The authors then look at both the kernel and image of this map to get isomorphism conditions between two of these algebras. This allows them to classify the regular nuclear Bernstein algebras of types \((n+1,1)\) and \((n+1,n(n+1)/2-1)\) over the real and complex fields. Finally, the real regular nuclear Bernstein algebras of type \((n+1,1)\) with a so called stochastic realization are determined too.
scientific article; zbMATH DE number 931896