Dynastic order Dynastic order A dynastic order, monarchical order, or house order, is an order under royal patronage, bestowed by the head of a currently or formerly sovereign royal family as legitimate fons honorum. These are often considered part of the cultural patrimony of the royal family. They are orders of chivalry, and orders of merit just as those distributed by sovereign states, but dynastic orders were often founded or maintained to reward service to a monarch, or the monarch's subsequent dynasty. An example of this difference is seen between the Royal Victorian Order, in which appointments are made as a personal
Restricted Lie algebra Restricted Lie algebra In mathematics, a restricted Lie algebra is a Lie algebra together with an additional ""p" operation." Let "L" be a Lie algebra over a field "k" of characteristic "p>0". A "p" operation on "L" is a map formula_1 satisfying If the characteristic of "k" is 0, then "L" is a restricted Lie algebra where the "p" operation is the identity map. For any associative algebra "A" defined over a field of characteristic "p", the bracket operation formula_11 and "p" operation formula_12 make "A" into a restricted Lie algebra formula_13. Let "G" be an algebraic group over a