On Lie powers of regular modules in characteristic 2

L. G. Kovács; Ralph Stöhr

Displaying similar documents to “On Lie powers of regular modules in characteristic 2”

Lie powers of infinite-dimensional modules.

Bryant, R.M. (2009)

Beiträge zur Algebra und Geometrie

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Lie commutators in a free diassociative algebra

A.S. Dzhumadil&amp;#039;daev, N.A. Ismailov, A.T. Orazgaliyev (2020)

Communications in Mathematics

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We give a criterion for Leibniz elements in a free diassociative algebra. In the diassociative case one can consider two versions of Lie commutators. We give criterions for elements of diassociative algebras to be Lie under these commutators. One of them corresponds to Leibniz elements. It generalizes the Dynkin-Specht-Wever criterion for Lie elements in a free associative algebra.

Composition-diamond lemma for modules

Yuqun Chen, Yongshan Chen, Chanyan Zhong (2010)

Czechoslovak Mathematical Journal

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We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra $s l_{2}$ , the Verma module over a Kac-Moody algebra, the...

On representations of restricted Lie superalgebras

Yu-Feng Yao (2014)

Czechoslovak Mathematical Journal

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Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type $A (n | 0)$ , the baby Verma modules $Z_{χ} (λ)$ are proved to be simple for any regular nilpotent $p$ -character $χ$ and typical weight $λ$ . Moreover, we obtain the dimension formulas for projective covers of simple modules with $p$ -characters of standard Levi form.

On the ghost centre of Lie superalgebras

Maria Gorelik (2000)

Annales de l'institut Fourier

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We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.

Formal de Rham theory: irreducible representations of finite simple Lie pseudoalgebras

Alessandro D'Andrea (2004)

Bollettino dell'Unione Matematica Italiana

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In this communication, I recall the main results [BDK1] in the classification of finite Lie pseudoalgebras, which generalize several previously known algebraic structures, and announce some new results [BDK2] concerning their representation theory.