Centers of higher degree trace forms

作者：Shapiro Daniel B^*; O'Ryan Manuel

来源：Journal of Pure and Applied Algebra, 2013, 217(12): 2263-2273.

DOI：10.1016/j.jpaa.2013.03.005

If theta is a regular, symmetric d-linear form on a vector space V, the center of (V, theta) is the set of linear maps f : V -> V symmetric relative to theta. If d > 2, it is well known that this center is a commutative subalgebra of End(V).
When A is a Frobenius algebra with "trace" l, we investigate the trace form phi(x) = l(x(d)) on A. When A is commutative, A itself is the center of that trace form and the orthogonal group O(V, phi) is closely related to the automorphism group of the algebra A. In noncommutative cases, trace forms are more difficult to analyze. If A is a symmetric algebra, the center of the degree d trace form on A turns out to be N(A(+)), the nucleus of the induced Jordan algebra.

• 出版日期2013-12