We study the set of generalized principal $\mathfrak{g}$-logarithms of any matrix belonging to a connected SVD-closed subgroup $G$ of $U_n$, with Lie algebra $\mathfrak{g}$. This set is a non-empty disjoint union of a finite number of subsets diffeomorphic to homogeneous spaces, and it is related to a suitable set of minimizing geodesics. Many particular cases for the group $G$ are explicitly analysed.
SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics / Donato Pertici; Alberto Dolcetti. - STAMPA. - (2022), pp. 1-23.
SVD-closed subgroups of the unitary group: generalized principal logarithms and minimizing geodesics
Donato Pertici;Alberto Dolcetti
2022
Abstract
We study the set of generalized principal $\mathfrak{g}$-logarithms of any matrix belonging to a connected SVD-closed subgroup $G$ of $U_n$, with Lie algebra $\mathfrak{g}$. This set is a non-empty disjoint union of a finite number of subsets diffeomorphic to homogeneous spaces, and it is related to a suitable set of minimizing geodesics. Many particular cases for the group $G$ are explicitly analysed.File in questo prodotto:
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