In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.

Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras / Faccin, Paolo. - (2014), pp. 1-89.

Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras

Faccin, Paolo
2014-01-01

Abstract

In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra.
2014
XXVI
2012-2013
Matematica (29/10/12-)
Mathematics
De Graaf, Willem A.
no
Inglese
Settore MAT/02 - Algebra
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/368142
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