Finite Order Automorphisms And Real Forms Of Affine Kac Moody Algebras In The Smooth And Algebraic Category

Finite Order Automorphisms and Real Forms of Affine Kac-Moody Algebras in the Smooth and Algebraic Category

Heintze and Gross discuss isomorphisms between smooth loop algebras and of smooth affine Kac-Moody algebras in particular, and automorphisms of the first and second kinds of finite order. Then they consider involutions of the first and second kind, and make the algebraic case. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).

Finite Order Automorphisms and Real Forms of Affine Kac-Moody Algebras in the Smooth and Algebraic Category

Classification and Structure Theory of Lie Algebras of Smooth Sections

Lie groups and their "derived objects", Lie algebras, appear in various fields of mathematics and physics. At least since the beginning of the 20th century, and after the famous works of Wilhelm Killing, Elie Cartan, Eugenio Elia Levi, Anatoly Malcev and Igor Ado on the structure of finite-dimensional Lie algebras, the classification and structure theory of infinite-dimensional Lie algebras has become an interesting and fairly vast field of interest. This dissertation focusses on the structure of Lie algebras of smooth and k-times differentiable sections of finite-dimensional Lie algebra bundles, which are generalizations of the famous and well-understood affine Kac-Moody algebras. Besides answering the immediate structural questions (center, commutator algebra, derivations, centroid, automorphism group), this work approaches a classification of section algebras by homotopy theory. Furthermore, we determine a universal invariant symmetric bilinear form on Lie algebras of smooth sections and use this form to define a natural central extension which is universal, at least in the case of Lie algebra bundles with compact base manifold.