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- Restricted cohomology (3)
- Irreducible module (2)
- Loewy layer (2)
- Principal block (2)
- Projective indecomposable module (2)
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- Abelian p-ideal (1)
- Cohomology (1)
- Direct Summand (1)
- Free module (1)
- Heisenberg algebra (1)
- Isomorphism Class (1)
- Leibniz cohomologyChevalley-Eilenberg cohomologySpectral sequenceCohomological vanishingInvariant symmetric bilinear formCartan-Koszul mapComplete Lie algebraRigid Leibniz algebraWitt algebraBorel subalgebraParabolic subalgebraSemi-simple Leibniz algebraSecond Whitehead lemmaOuter derivation (1)
- Maximal Dimension (1)
- Maximal Torus (1)
- Maximal abelian p-ideal (1)
- Maximal p-ideal (1)
- Multiplicity of a split strongly abelian p-chief factor (1)
- Nilpotent Lie algebra (1)
- Nilpotent outer restricted derivation (1)
- Outer restricted derivation (1)
- P-chief factor (1)
- P-supplement (1)
- P-unipotent restricted Lie algebra (1)
- Projective Cover (1)
- Restricted Lie algebra (1)
- Restricted derivation (1)
- Solvable Lie algebra (1)
- Solvable restricted Lie algebra (1)
- Split abelian chief factor (1)
- Split p-chief factor (1)
Articles 1 - 6 of 6
Full-Text Articles in Other Mathematics
On Leibniz Cohomology, Jorg Feldvoss, Friedrich Wagemann
On Leibniz Cohomology, Jorg Feldvoss, Friedrich Wagemann
University Faculty and Staff Publications
In this paper we prove the Leibniz analogue of Whitehead's vanishing theorem for the Chevalley-Eilenberg cohomology of Lie algebras. As a consequence, we obtain the second Whitehead lemma for Leibniz algebras. Moreover, we compute the cohomology of several Leibniz algebras with ad joint or irreducible coefficients. Our main tool is a Leibniz analogue of the Hochschild-Serre spectral sequence, which is an extension of the dual of a spectral sequence of Pirashvili for Leibniz homology from symmetric bimodules to arbitrary bimodules.
Restricted Lie Algebras With Maximal 0-Pim, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
Restricted Lie Algebras With Maximal 0-Pim, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
University Faculty and Staff Publications
In this paper it is shown that the projective cover of the trivial irreducible module of a finite-dimensional solvable restricted Lie algebra is induced from the one dimensional trivial module of a maximal torus. As a consequence, the number of the isomorphism classes of irreducible modules with a fixed p-character for a finite-dimensional solvable restricted Lie algebra L is bounded above by p MT(L), where MT(L) denotes the maximal dimension of a torus in L. Finally, it is proved that in characteristic p > 3 the projective cover of the trivial irreducible L-module is induced …
Erratum To “Support Varieties And Representation Type Of Small Quantum Groups”, Jorg Feldvoss, Sarah Witherspoon
Erratum To “Support Varieties And Representation Type Of Small Quantum Groups”, Jorg Feldvoss, Sarah Witherspoon
University Faculty and Staff Publications
Some of the general results in the paper require an additional hypothesis, such as quasitriangularity. Applications to specific types of Hopf algebras are correct, as some of these are quasitriangular, and for those that are not, the Hochschild support variety theory may be applied instead.
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 …
Outer Restricted Derivations Of Nilpotent Restricted Lie Algebras, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
Outer Restricted Derivations Of Nilpotent Restricted Lie Algebras, Jorg Feldvoss, Salvatore Siciliano, Thomas Weigel
University Faculty and Staff Publications
In this paper we prove that every finite-dimensional nilpotent restricted Lie algebra over a field of prime characteristic has an outer restricted derivation whose square is zero unless the restricted Lie algebra is a torus or it is one-dimensional or it is isomorphic to the three-dimensional Heisenberg algebra in characteristic two as an ordinary Lie algebra. This result is the restricted analogue of a result of Tôgô on the existence of nilpotent outer derivations of ordinary nilpotent Lie algebras in arbitrary characteristic and the Lie-theoretic analogue of a classical group-theoretic result of Gaschütz on the existence of p-power automorphisms …