Celebratio Mathematica

G. Benkart: “A Kac–Moody bibliography and some related references,” pp. 111–135 in Lie algebras and related topics (26 June–6 July 1984, Windsor, ON). Edited by D. J. Britten, F. W. Lemire, and R. V. Moody. CMS Conference Proceedings 5. American Mathematical Society (Providence, RI), 1986. MR 832196 Zbl 0578.17013 incollection

Frank W. Lemire	Related
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Daniel John Britten	Related

G. Benkart: “Cartan subalgebras in Lie algebras of Cartan type,” pp. 157–187 in Lie algebras and related topics (26 June–6 July 1984, Windsor, ON). Edited by D. J. Britten, F. W. Lemire, and R. V. Moody. CMS Conference Proceedings 5. American Mathematical Society (Providence, RI), 1986. MR 832198 Zbl 0581.17006 incollection

The known finite dimensional simple Lie algebras over an algebraically closed field of characteristic \( p\geq 7 \) are either classical (analogues of complex Lie algebras) or of Cartan type. Each Lie algebra \( L \) of Cartan type possesses a certain maximal subalgebra \( L_0 \) which is invariant under the automorphisms of \( L \), and every Cartan subalgebra \( L_0 \) is a Cartan subalgebra of \( L \). The main result of this work is to show that the Cartan subalgebras of \( L_0 \) are conjugate under the group generated by the generalized exponential mappings defined by \[ E^z = 1 + \sum_{j=1}^{p-1} \left(\prod_{\nu = 1}^j (\nu \vert -\psi)^{-1}\right)(adz)^j \] where \( z\in L_0 \) has \( (adz)^{p^k} = 0 \), and where \[ \psi = (adz)^p + \cdots + (adz)^{p^{k-1}} .\] As a consequence, all the Cartan subalgebras of \( L \) in \( L_0 \) have the same dimension, and this dimension is computed for each type of algebra.

Frank W. Lemire	Related
Robert V. Moody	Related
Daniel John Britten	Related

G. M. Benkart and R. V. Moody: “Derivations, central extensions, and affine Lie algebras,” Algebras Groups Geom. 3 : 4 (1986), pp. 456–492. MR 901810 Zbl 0619.17014 article

G. Benkart and A. Elduque: “Lie superalgebras graded by the root systems \( C(n) \), \( D(m,n) \), \( D(2,1;\alpha) \), \( F(4) \), \( G(3) \),” Canad. Math. Bull. 45 : 4 (2002), pp. 509–524. To Professor Robert Moody with our best wishes on his sixtieth birthday. MR 1941225 Zbl 1040.17026 article

Robert V. Moody	Related
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