Index of notation

The reference numbers indicate respectively the chapter, paragraph and number (or, occasionally, exercise).

$[x, y]$ (x, y elements of a Lie algebra): I.1.2. $g^0$ (g a Lie algebra): I.1.2. $gl(E), gl(n, K), sl(E), sl(n, K), t(n, K), st(n, K), n(n, K)$ (E a K-module): I.1.2. $ad_g x, ad x$ (x an element of a Lie algebra g): I.1.2. $[a, b], [z, a], [a, z]$ (a, b submodules, z an element of a Lie algebra): I.1.4. $\mathscr{D}g, \mathscr{D}^k g, \mathscr{C}^k g$ (g a Lie algebra): I.1.5. $\mathscr{C}_k g$ (g a Lie algebra): I.1.6. $af(M)$ (M a K-module): I.1.8. $g_{(K_1)}$ (g a Lie algebra): I.1.9. $U_+, U_0$ (U the enveloping algebra of a Lie algebra): I.2.1. $T^n, S^n, S'^n$ : I.2.5. $T_n, U_n, G^n$ : I.2.6. $x_M$ (x an element of a Lie algebra g, M a g-module): I.3.1. $e^u, \exp u$ (u a nilpotent endomorphism of a vector space over a field of characteristic 0): I.6.8. $C(\rho)$ ($\rho$ a representation of a Lie algebra): I.7.1. $\mathscr{C}^\infty g, \mathscr{D}^\infty g$: I.1, Exercise 14. $x^{[n]}$: I.1, Exercise 20. $GL(n, K)$ (formal group): I.1, Exercise 25. $o(\Phi)$: I.1, Exercise 26. $C^p(g, M), C^*(g, M), i(y), \theta(x), d, Z^p(g, M), B^p(g, M), H^p(g, M), H^*(g, M)$ (g a Lie algebra, M a g-module): I.3, Exercise 12. $sp(2n, K)$: I.6, Exercise 25. $K$: II.Conventions. $g, U = Ug, \sigma: g \to Ug$: II.1. $\varepsilon, c, u, \pi_u, \eta_u, c_u^+$ : II.1.1.

$E, E^+$ : II.1.1. $P(E), \pi, \eta, c^+$ : II.1.6. $S(g), c_s, \eta$ : II.1.5. $f_E : U(P(E)) \to E$ : II.1.6. $M(X), l(w), Lib(X) = Lib_K(X)$ : II.2.1. $L(X) = L_K(X)$ : II.2.2. $\varphi : X \to L(X)$ : II.2.2. $(a, r)$ : II.2.3. $L(u)$ : II.2.5. $Lib^\delta(X), L^\delta(X), L^n(X)$ : II.2.6. $P_n$ : II.2.7. $C^n(g)$ : II.2.7. $H, d_y$ : II.2.10. $\overline{w}= \Psi'(w)$ : II.2.11. $A(X) = A_K(X), A^+(X), Mo(X)$ : II.3. $\pi$ : II.3.2. $(G_\alpha), (G_\alpha^+)$ : II.4.1. $v$ : II.4.2. $gr(G), gr_\alpha(G)$ : II.4.3. $F(X), A(X), A^n(X)$ : II.5. $\hat{A}(X), \omega$ : II.5.1. $\varepsilon(a)$ : II.5.2. $l(x), exp(x), log(y)$ : II.6.1. $e(X), l(X)$ : II.6.1. $\hat{L}(X)$ : II.6.2. $a \oplus b$ : II.6.2. $H, H_n, H_{rs}$ : II.6.4. $\tilde{H}, \Omega$ : II.7.2. $A, exp_A, log_A, \hat{P}(A^t, A)$ : II.7.3. $v, \theta= \frac{1}{p - 1}$ : II.8. $S(n)$ : II.8.1. $h(x, y)$ : II.8.3. $G_R$ : II.8.4. $\mu(n)$ : II.App. $e, e_G, \gamma(g), \delta(g), Int(g), f^*$ : III.Conventions. $GL(E), GL(n, K)$ : III.1.1, III.3.10. $G^\vee$ : III.1.2. $\tau(g), \rho(x)$ : III.1.5. $(G, g, \theta, m)$ : III.1.10. $T(m)$ : III.2.1. $T(G), T(\varphi)$ : III.2.2. $t \ast t'$ : III.3.1, III.3.18.

$U(G), U^+(G), U_s(G), U_s^+(G)$: III.3.1, III.3.18. $T_g^{(s)}(G), T_g^{(\infty)}(G), \mathscr{T}^{(\infty)}(G)$: III.3.1, III.3.18. $t \ast f$ : III.3.4, III.3.18. $D_t$ : III.3.5, III.3.18. $L_t, R_t$ : III.3.6, III.3.18. $L(G)$: III.3.7, III.3.18. $L(\varphi)$: III.3.8, III.3.18. $\langle t, f \rangle$ : III.3.9, III.3.18. $SL(E)$: III.3.10. $Ad, Ad(g)$: III.3.12. $[\alpha]^2$ : III.3.14. $mod(\omega)_u, mod \varphi$: III.3.16. $f^{-1}.df$: III.3.17, III.3.18. $H$ : III.4.2. $g^t, \varpi(x)$: III.4.3. $x.y, x^{[n]}$ : III.5. $c_{\alpha\beta\gamma}, B(x, y)$: III.5.1. $e_\alpha$ : III.5.2. $\psi_j, \psi_{p,m}, \binom{t}{i}$ : III.5.3. $E(x), L(x)$: III.5.4. $P_M, x.y$ : III.6.2. $Ad(a) = Int(a)$ : III.6.2. $exp, exp_G$: III.6.4. $Ad(G) = Int(L(G))$ : III.6.4. $L(\rho)$ : III.6.5. $\bar{G}$ : III.6.10. $A, m, p$ : III.7. $G(a)$: III.7.4. $h_n$ : III.7.5. $G_f, \log_G, \log$ : III.7.6. $\overline{D}^tG, \overline{C}^tG$: III.9.1. $Z_G(A), Z_G(a), \delta_G(A), \delta_G(a)$ : III.9.3. $N_G(A), N_G(a), n_g(a)$ : III.9.4. $R, N, r, n$ : III.9.7. $\pi_1 \otimes \cdots \otimes \pi_n, \mathbf{T}(\pi), S(\pi), \wedge(\pi), \mathbf{T}^n(\pi), S^n(\pi), \wedge^n(\pi)$: III.App.