Department of Mathematics
Title : The LU-decomposition of matrices and algebraic groups
| Speaker: Don Taylor Affiliation: University of Sydney Time: 13:00 Tuesday, 16 April, 2013 Location: 303-412 |
Abstract
| The factorisation of a matrix as a product of a lower triangular by an upper triangular matrix (up to a permutation of the rows) is a form of 'Gauss elimination'. The lower and upper triangular matrices are themselves products of elementary matrices representing row operations. This is described in connection with machine computation in a 1948 paper of Alan Turing. The generalisation of this decomposition to classical groups by Bruhat (1954) and then to semisimple algebraic groups by Chevalley (1955) led to the introduction of the general notion of a BN-pair by Jacques Tits. In joint work with Arjeh Cohen and Scott Murray a general row reduction algorithm has been developed to write a matrix acting on a highest weight representation of a group of Lie type as a word in the Steinberg generators of the group. This talk will focus on examples and on aspects of the Magma implementation relevant to the recent work of Liebeck and O'Brien on the recognition of finite groups of Lie type. |
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Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
