Analogue of a Reductive Algebraic Monoid Whose Unit Group Is a Kac-Moody Group.

Intro -- Contents -- Introduction -- Contents -- Chapter 1. Preliminaries -- 1.1. Kac-Moody algebras, Kac-Moody groups and the algebra of strongly regular functions -- 1.2. A generalization of affine toric varieties -- Chapter 2. The monoid G and its structure -- 2.1. The face lattice of the Tits cone -- 2.2. The definition of the monoid G -- 2.3. Formulas for computations in G -- 2.4. The unit regularity of G -- 2.5. The Weyl monoid W and the monoids T, N -- 2.6. Some double coset partitions of G -- 2.7. Constructing G from the twin root datum -- 2.8. The action of G on the admissible modules of ο -- 2.9. The submonoids G[sub(J)] (J ⊆ I) -- 2.10. The monoid G for a decomposable matrix A -- Chapter 3. An algebraic geometric setting -- 3.1. Varieties and pnc-varieties -- 3.2. Weak (pnc-)algebraic monoids -- Chapter 4. A generalized Tannaka-Krein reconstruction -- Chapter 5. The proof of G = G and some other theorems -- 5.1. The coordinate rings and closures of T, T[sub(J)] (J ⊆ I), and T[sub(rest)] -- 5.2. The orbits G[sub(J)](L(Λ)[sub(Λ)]) (J ⊆ I) and G (L(Λ)[sub(Λ)]) -- 5.3. The coordinate rings and closures of U[sup(+)][sub(J)], (U[sup(J)])[sup(+)] (J ⊆ I) -- 5.4. The closures of G[sub(J)] (J ⊆ I) and G -- 5.5. The closures of N[sub(J)] (J ⊆ I) and N -- 5.6. The openness of the unit group -- 5.7. The Kac-Peterson-Slodowy part of SpecmF [G] -- Chapter 6. The proof of Lie(G) ≅ g -- 6.1. The Lie algebra of T -- 6.2. The Lie algebras of U[sup(+)] and U[sup(-)] -- 6.3. The Lie algebra of G -- Bibliography.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.