Iodine (medical use) Iodine (medical use) Iodine is used to treat and prevent iodine deficiency and as an antiseptic. For iodine deficiency it can be given by mouth or injection into a muscle. As an antiseptic it may be used on wounds that are wet or to disinfect the skin before surgery. Common side effects when applied to the skin include irritation and discoloration. When taken by mouth or injection side effects may include allergic reactions, goitre, and thyroid dysfunction. Use during pregnancy is recommended in regions where deficiency is common, otherwise it is not recommended. Iodine is an essential trace element. In
Trace field of a representation Trace field of a representation In mathematics, the trace field of a linear group is the field generated by the traces of its elements. It is mostly studied for Kleinian and Fuchsian groups, though related objects are used in the theory of lattices in Lie groups, often under the name "field of definition". Fuchsian groups are discrete subgroups of formula_1. The trace of an element in formula_1 is well-defined up to sign (by taking the trace of an arbitrary preimage in formula_3) and the "trace field" of formula_4 is the field generated over formula_5 by the traces of all elements