Order of the Phoenix (fictional organisation) name, Lupin, refers to the Latin word "lupus", which means wolf. Alastor "Mad-Eye" Moody is perhaps the most famous Auror in the modern times of the Wizarding World, single-handedly responsible for capturing numerous wizard criminals. He is also said never to have killed his quarry, even when permitted to do so, unless he had no other choice. Moody's face is badly scarred; he has lost several body parts while fighting Dark wizards, including his left eye, lower left leg, and part of his nose; and he is cautious – some characters might say paranoid – in that he refuses to
Kac–Moody algebra one which is now infinite dimensional. Simultaneously, Z-graded Lie algebras were being studied in Moscow where I. L. Kantor introduced and studied a general class of Lie algebras including what eventually became known as Kac–Moody algebras. Victor Kac was also studying simple or nearly simple Lie algebras with polynomial growth. A rich mathematical theory of infinite dimensional Lie algebras evolved. An account of the subject, which also includes works of many others is given in (Kac 1990). See also (Seligman 1987). A Kac–Moody algebra may be defined by first giving the following: The Kac–Moody algebra is then the Lie algebra