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Restricted Lazard elimination and modular Lie powers

Part of: Representation theory of groups Lie algebras and Lie superalgebras

Published online by Cambridge University Press:  09 April 2009

Ralph Stöhr
Ralph Stöhr
Affiliation:
Department of MathematicsUMIST, PO Box 88, Manchester M60 1QD, United Kingdom e-mail: [email protected]
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Abstract

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We exhibit a variation of the Lazard Elimination theorem for free restricted Lie algebras, and apply it to two problems about finite group actions on free Lie algebras over fields of positive characteristic.

MSC classification

Secondary: 17B01: Identities, free Lie (super)algebras 20C20: Modular representations and characters
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 71 , Issue 2 , October 2001 , pp. 259 - 278
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Yu., A. Bakhturin, Identities in Lie algebras (Nauka, Moscow, 1985), in Russian: English translation: (VNU Sci. Press, Utrecht, 1987).Google Scholar
[2]Bourbaki, N., Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Gropues de Lie (Hermann, Pairs, 1972).Google Scholar
[3]Bryant, R. M., ‘Cyclic groups acting on free Lie algebras’, in: Geometry and cohomology in group theory (Durham, 1994) (eds. Kropholler, P. H., Niblo, G. A. and Stöhr, R.) (Cambridge Univ. Press, Cambridge, 1998) pp. 39–44.CrossRefGoogle Scholar
[4]Bryant, R. M., Kovács, L. G. and Stöhr, R., ‘Free Lie algebras as modules for sysmmetric groups’, J. Austral. Math. Soc. Ser. A 67 (1999), 143–156.CrossRefGoogle Scholar
[5]Bryant, R. M., Kovács, L. G. and Stöhr, R., ‘Lie powers of modules for groups of prime order’, Proc. London Math. Soc., to appear.Google Scholar
[6]Bryant, R. M., Kovács, L. G. and Stöhr, R., ‘Invariant bases for free Lie rings’, Quart. J. Math. Oxford, to appear.Google Scholar
[7]Bryant, R. M., Kovács, L. G. and Stöhr, R., ‘Lie powers of the natural module for GL(2, p)’, in preparation.Google Scholar
[8]Bryant, R. M. and Michos, I. C., ‘Lie powers of free modules for certain groups of prime power order’, J. Austral. Math. Soc., to appear.Google Scholar
[9]Bryant, R. M. and Stöhr, R., ‘Fixed points of automorphisms of free Lie algebras’, Arch. Math. (Basel) 67 (1996), 281–289.CrossRefGoogle Scholar
[10]Bryant, R. M. and Stöhr, R., ‘On the module structure of free Lie algebras’, Trans. Amer. Math. Soc. 352 (2000), 901–934.CrossRefGoogle Scholar
[11]Guilfoyle, S., On Lie powers of modules for cyclic groups (Ph.D. Thesis, Manchester, 2000).Google Scholar
[12]Guilfoyle, S. and Stöhr, R., ‘Invariant bases for free Lie algebras’, J. Algebra 204 (1998), 337–346.CrossRefGoogle Scholar
[13]Kovács, L. G. and Stöhr, R., ‘Module structure of the free Lie ring on three generators’, Arch. Math. (Basel) 73 (1999), 182–185.CrossRefGoogle Scholar
[14]Kovács, L. G. and Stöhr, R., ‘Lie powers of the natural module for GL(2)’, J. Algebra 229 (2000), 435–462.CrossRefGoogle Scholar
[15]Michos, I. C., Finite groups acting on free Lie algebras (Ph. D. Thesis, Manchester, 1998).Google Scholar
[16]Michos, I. C., ‘Integral Lie Powers of a lattice for the cyclic group of order 2’, Arch. Math. (Basel) 75 (2000), 188–194.CrossRefGoogle Scholar
[17]Short, M. W., ‘A conjecture about free Lie algebras’, Comm. Algebra 23 (1995), 3051–3057.CrossRefGoogle Scholar
[18]The Kourovka Notebook: Unsolved problems in group theory, 11th edition, (Novosibirsk, 1990).Google Scholar