It is shown that for the restricted Zassenhaus algebra (formula presented)= (formula presented)(1; n), n > 1, defined over an algebraically closed field F of characteristic 2, any projective indecomposable restricted (formula presented)-module has maximal possible dimension 22-1n, and thus is isomorphic to some induced module idnt(formula presented) (F(μ)) for some torus of maximal dimension t. This phenomenon is in contrast to the behavior of finite-dimensional non-solvable restricted Lie algebras in characteristic p > 3 (cf. Feldvoss et al. Restricted Lie algebras with maximal 0-pim, 2014, Theorem 6.3).
Lancellotti, B., Weigel, T. (2015). The p.i.m.s for the restricted Zassenhaus algebras in characteristic 2. ARCHIV DER MATHEMATIK, 104(4), 333-340 [10.1007/s00013-015-0748-3].
The p.i.m.s for the restricted Zassenhaus algebras in characteristic 2
LANCELLOTTI, BENEDETTA
;WEIGEL, THOMAS STEFAN
2015
Abstract
It is shown that for the restricted Zassenhaus algebra (formula presented)= (formula presented)(1; n), n > 1, defined over an algebraically closed field F of characteristic 2, any projective indecomposable restricted (formula presented)-module has maximal possible dimension 22-1n, and thus is isomorphic to some induced module idnt(formula presented) (F(μ)) for some torus of maximal dimension t. This phenomenon is in contrast to the behavior of finite-dimensional non-solvable restricted Lie algebras in characteristic p > 3 (cf. Feldvoss et al. Restricted Lie algebras with maximal 0-pim, 2014, Theorem 6.3).
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