arXiv subjects

Benjamin H. Smith

Publications and source records attributed to Benjamin H. Smith.

2 recordsLinked to original sources

arXiv2015

Singular $G$-monopoles on $S^1\times Σ$

This article provides an account of the functorial correspondence between irreducible singular $G$-monopoles on $S^1\times Σ$ and $\vec{t}$-stable meromorphic pairs on $Σ$. The main theorem of [1] is thus generalized here from unitary to arbitrary compact, connected gauge groups. The required distinctions and similarities for unitary versus arbitrary gauge are clearly outlined and many parallels are drawn for easy transition. Once the correspondence theorem is complete, the spectral decomposition is addressed.

math.DG↗

arXiv2007

Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities

We construct six unitary trace invariants for 2 by 2 quaternionic matrices which separate the unitary similarity classes of such matrices, and show that this set is minimal. We prove two quaternionic versions of a well known characterization of triangularizable subalgebras of matrix algebras over an algebraically closed field. Finally we consider the problem of describing the semi-algebraic set of pairs (X,Y) of quaternionic n by n matrices which are simultaneously triangularizable. Even the case n=2, which we analyze in more detail, remains unsolved.

math.AC↗