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On Some Twisted Chevalley Groups Over Laurent Polynomial Rings

Published online by Cambridge University Press:  20 November 2018

Jun Morita
Jun Morita*
Affiliation:
University of Tsukuba, Ibaraki, Japan
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We let Z denote the ring of rational integers, Q the field of rational numbers, R the field of real numbers, and C the field of complex numbers.

For elements e and f of a Lie algebra, [e,f] denotes the bracket of e and f. A generalized Cartan matrix C = (cij ) is a square matrix of integers satisfying cii = 2, cij ≦ 0 if i ≠ j, cij = 0 if and only if cji = 0. For any generalized Cartan matrix C = (cij ) of size l × l and for any field F of characteristic zero, denotes the Lie algebra over F generated by 3l generators e 1, …, el , h 1, …, hl , f 1, …, fl with the defining relations

for all i, j,

for distinct i, j.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 5 , 01 October 1981 , pp. 1182 - 1201
Copyright
Copyright © Canadian Mathematical Society 1981

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