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Full-Text Articles in Other Mathematics
Split Strongly Abelian P-Chief Factors And First Degree Restricted Cohomology, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
Split Strongly Abelian P-Chief Factors And First Degree Restricted Cohomology, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
University Faculty and Staff Publications
In this paper we investigate the relation between the multiplicities of split strongly abelian p-chief factors of finite-dimensional restricted Lie algebras and first degree restricted cohomology. As an application we obtain a characterization of solvable restricted Lie algebras in terms of the multiplicities of split strongly abelian p-chief factors. Moreover, we derive some results in the representation theory of restricted Lie algebras related to the principal block and the projective cover of the trivial irreducible module of a finite-dimensional restricted Lie algebra. In particular, we obtain a characterization of finite-dimensional solvable restricted Lie algebras in terms of the second Loewy …
Split Abelian Chief Factors And First Degree Cohomology For Lie Algebras, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
Split Abelian Chief Factors And First Degree Cohomology For Lie Algebras, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
University Faculty and Staff Publications
In this paper we investigate the relation between the multiplicities of split abelian chief factors of finite-dimensional Lie algebras and first degree cohomology. In particular, we obtain a characterization of modular solvable Lie algebras in terms of the vanishing of first degree cohomology or in terms of the multiplicities of split abelian chief factors. The analogues of these results are well known in the modular representation theory of finite groups. An important tool in the proof of these results is a refinement of a non-vanishing theorem of Seligman for the first degree cohomology of non-solvable finite-dimensional Lie algebras in prime …