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Carter subgroups in the group of units of an associative algebra

Published online by Cambridge University Press:  17 April 2009

Thorsten Bauer  and
Salvatore Siciliano
Thorsten Bauer
Affiliation:
Schuetzenwall 43, D–24114 Kiel, Germany, e-mail: thorsten.bauer@ppi.de
Salvatore Siciliano
Affiliation:
Dipartimento di Matematica “E. De Giorgi”, Università degli Studi di Lecce, Via Provinciale Lecce-Arnesano, 73100-Lecce, Italy, e-mail: salvatore.siciliano@unile.it
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In this paper we examine some properties of the Carter subgroups in the group of units of certain associative algebras. A description of the Carter subgroups in the case of a solvable associative algebra is obtained. Moreover, given an associative algebra A, we study relationships between the Cartan subalgebras of the Lie algebra associated with A and the Carter subgroups of the group of units of A.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 3 , June 2005 , pp. 471 - 478
Copyright
Copyright © Australian Mathematical Society 2005

References

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