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- Irreducible module (2)
- Loewy layer (2)
- Principal block (2)
- Projective indecomposable module (2)
- Restricted cohomology (2)
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- Cohomology (1)
- Leibniz cohomology; Chevalley-Eilenberg cohomology; Hochschild cohomology; cohomological (non-)vanishing; Fitting decomposition; semi-simple Leibniz algebra; nilpotent Leibniz algebra; inner derivation; infinitesimal deformation; rigid Leibniz algebra; supersolvable Leibniz algebra; solvable Leibniz algebra; right faithful Leibniz bimodule; maximal subalgebra; Frattini subalgebra; minimal ideal; right self-centralizing ideal (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)
- Multiplicity of a split strongly abelian p-chief factor (1)
- P-chief factor (1)
- Solvable Lie algebra (1)
- Solvable restricted Lie algebra (1)
- Split abelian chief factor (1)
- Split p-chief factor (1)
- Strongly abelian p-chief factor (1)
- Transgression (1)
Articles 1 - 8 of 8
Full-Text Articles in Algebraic Geometry
On The Cohomology Of Solvable Leibniz Algebras, Jorg Feldvoss, Friedrich Wagemann
On The Cohomology Of Solvable Leibniz Algebras, Jorg Feldvoss, Friedrich Wagemann
University Faculty and Staff Publications
This paper is a sequel to J. Feldvoss and F. Wagemann: On Leibniz cohomology, (2021), where we mainly consider semisimple Leibniz algebras. It turns out that the analogue of the Hochschild-Serre spectral sequence for Leibniz cohomology cannot be applied to many ideals, and therefore this spectral sequence seems not to be applicable for computing the cohomology of non-semi-simple Leibniz algebras. The main idea of the present paper is to use similar tools as developed by Farnsteiner for Hochschild cohomology (see R. Farnsteiner: On the cohomology of associative algebras and Lie algebras (1987) and R. Farnsteiner: On the vanishing of homology …
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.
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 …
Injective Modules And Prime Ideals Of Universal Enveloping Algebras, Jorg Feldvoss
Injective Modules And Prime Ideals Of Universal Enveloping Algebras, Jorg Feldvoss
University Faculty and Staff Publications
In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also elaborate on some of their analogues for solvable Lie algebras over fields of characteristic zero. It turns out that analogous results in both cases are often quite similar and resemble those familiar from commutative ring theory.
Existence Of Solutions Of The Classical Yang-Baxter Equation For A Real Lie Algebra, Jorg Feldvoss
Existence Of Solutions Of The Classical Yang-Baxter Equation For A Real Lie Algebra, Jorg Feldvoss
University Faculty and Staff Publications
We characterize finite-dimensional Lie algebras over the real numbers for which the classical Yang-Baxter equation has a non-trivial skew-symmetric solution (resp. a non-trivial solution with invariant symmetric part). Equivalently, we obtain a characterization of those finite-dimensional real Lie algebras which admit a non-trivial (quasi-) triangular Lie bialgebra structure.
Homological Topics In The Representation Theory Of Restricted Lie Algebras, Jorg Feldvoss
Homological Topics In The Representation Theory Of Restricted Lie Algebras, Jorg Feldvoss
University Faculty and Staff Publications
We present some recent developments in the application of homological methods to the representation theory of finite dimensional restricted Lie algebras.