Vertex Algebras and Integral Bases for the Enveloping Algebras of Affine Lie Algebras.
- 1st ed.
- 1 online resource (113 pages)
- Memoirs of the American Mathematical Society ; v.96 .
- Memoirs of the American Mathematical Society .
Intro -- Table of Contents -- 1 Introduction -- 2 Construction of the affine Lie algebras -- 2.1 A[sup((1)][sub(l)] (I≥1), D[sup((1)][sub(l)] (I≥1) and E[sup((1)][sub(l)] (I = 6,7,8) -- 2.2 B[sup((1)][sub(n)] (n≥2), C[sup((1)][sub(n)] (n≥2), F[sup((1)][sub(4)] -- 2.3 A[sup((2)][sub(2n-1)] (n≥2), D[sup((2)][sub(n+1)] (n≥2), E[sup((2)][sub(6)] -- 2.4 G[sup((1)][sub(2)] -- 2.5 D[sup((3)][sub(4)] -- 2.6 A[sup((2)][sub(2n)] (n≥1) -- 3 The Main Theorem -- 3.1 Integral bases of the universal enveloping algebras of the affine Lie algebras -- 3.2 Exponential identities for the simply-laced affine Lie algebras -- 3.3 Exponential identities for B[sup((1)][sub(n)], C[sup((1)][sub(n)] and F[sup((1)][sub(4)] -- 3.4 Exponential identities for G[sup((1)][sub(2)] -- 3.5 Exponential identities for A[sup((2)][sub(2n-1)], D[sup((2)][sub(n+1)] and E[sup((2)][sub(6)] -- 3.6 Exponential identities for D[sup((3)][sub(4)] -- 3.7 Exponential identities for A[sup((2)][sub(2n)] -- 4 Vertex algebras and integral forms of the universal enveloping algebras of the affine Lie algebras -- 4.1 Vertex operator algebras and vertex algebras -- 4.2 Vertex operator representations of A[sup((l)][sub(1)] (I≥1),D[sup((1)][sub(l)](I≥1), E[sup((1)][sub(l)] (l = 6, 7, 8) -- 4.3 Schur polynomials and S(h[sup((-)][sub(Z)]) -- 4.4 An integral form for the vertex algebra V[sub(L')] -- 4.5 The embedding of the derived subalgebra l' in a module for V[sub(L')] -- 4.6 A family of irreducible integrable modules for l -- 4.7 A description for the unequal root length affine Lie algebras.