Lie Powers of the Natural Module for GL(2)

Kovács, László; Stöhr, Ralph

doi:10.1006/jabr.1998.7904

Cited by 11 publications

(16 citation statements)

References 23 publications

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“…By the next result, only finitely many Adams operations need to be found. With H as defined above, let q -\H/ C H {P)\ and let e be the least common multiple of 2pq and the orders of the p '-elements of G. The connection between Lie powers of K G-modules and Lie powers of KNmodules was a key factor in obtaining the results of [8,17] and [10]. The following theorem generalises one of the main qualitative results of [10].…”

Section: The General Casementioning

confidence: 91%

Modular Lie representations of finite groups

Bryant

2004

J. Aust. Math. Soc.

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Let K be a field of prime characteristic p and let G be a finite group with a Sylow p -subgroup of order p. For any finite-dimensional K G-module V and any positive integer n, let L"( V) denote the nth homogeneous component of the free Lie K-algebra generated by (a basis of) V. Then L n ( V) can be considered as a K G-module, called the nth Lie power of V. The main result of the paper is a formula which describes the module structure of L"( V) up to isomorphism.

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Section: The General Casementioning

confidence: 91%

Modular Lie representations of finite groups

Bryant

2004

J. Aust. Math. Soc.

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“…Then R 2 is the direct sum of two simple G L(2, 2)-modules (a trivial and a natural). We mention that in this case the module structure of L(x, y) has been completely determined in [17].…”

Section: Free Restricted Lie Algebras and Restricted Eliminationmentioning

confidence: 97%

Bases, filtrations and module decompositions of free Lie algebras

Stöhr¹

2008

Journal of Pure and Applied Algebra

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We use the technique known as elimination to devise some new bases of the free Lie algebra which (like classical Hall bases) consist of Lie products of left normed basic Lie monomials. Our bases yield direct decompositions of the homogeneous components of the free Lie algebra with direct summands that are particularly easy to describe: they are tensor products of metabelian Lie powers. They also give rise to new filtrations and decompositions of free Lie algebras as modules for groups of graded algebra automorphisms. In particular, we obtain some new decompositions for free Lie algebras and free restricted Lie algebras over fields of positive characteristic.

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“…This culminates in Theorem 6.4, from which the main results are easily deduced. With a view to further applications ( [7] in particular) we also include a modification of Theorem 6.4 (namely Proposition 6.5) which refers to the Lie powers of projective modules for the normalizer of a p-cycle in the symmetric group of degree p.…”

Section: Corollary 2 Let V Be a Free Zg-module Of Finite Rank Then mentioning

confidence: 99%