On real forms of Dubrovin-Ugaglia Poisson brackets

Dubrovin and Ugaglia introduced a holomorphic Poisson structure on the space of semisimple Frobenius manifolds, which is identified with the entries of an upper triangular matrix with ones on the diagonal. In this paper, we compute explicitly the real forms of the Dubrovin-Ugaglia Poisson structures, arising from the real forms of the Lie algebra son(C).(c) 2023 Elsevier B.V. All rights reserved.