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- 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)
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Articles 1 - 11 of 11
Full-Text Articles in Algebra
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.
Leibniz Algebras As Non-Associative Algebras, Jorg Feldvoss
Leibniz Algebras As Non-Associative Algebras, Jorg Feldvoss
University Faculty and Staff Publications
In this paper we define the basic concepts for left or right Leibniz algebras and prove some of the main results. Our proofs are often variations of the known proofs but several results seem to be new.
Some Problems In The Representation Theory Of Simple Modular Lie Algebras, Georgia Benkart, Jorg Feldvoss
Some Problems In The Representation Theory Of Simple Modular Lie Algebras, Georgia Benkart, Jorg Feldvoss
University Faculty and Staff Publications
No abstract provided.
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 …
Support Varieties And Representation Type Of Self-Injective Algebras, Jorg Feldvoss, Sarah Witherspoon
Support Varieties And Representation Type Of Self-Injective Algebras, Jorg Feldvoss, Sarah Witherspoon
University Faculty and Staff Publications
We use the theory of varieties for modules arising from Hochschild cohomology to give an alternative version of the wildness criterion of Bergh and Solberg [7]: If a finite dimensional self-injective algebra has a module of complexity at least 3 and satisfies some finiteness assumptions on Hochschild cohomology, then the algebra is wild. We show directly how this is related to the analogous theory for Hopf algebras that we developed in [23]. We give applications to many different types of algebras: Hecke algebras, reduced universal enveloping algebras, small half- quantum groups, and Nichols (quantum symmetric) algebras.
Support Varieties And Representation Type Of Small Quantum Groups, Jorg Feldvoss, Sarah Witherspoon
Support Varieties And Representation Type Of Small Quantum Groups, Jorg Feldvoss, Sarah Witherspoon
University Faculty and Staff Publications
In this paper, we provide a wildness criterion for any finite dimensional Hopf algebra with finitely generated cohomology. This generalizes a result of Farnsteiner to not necessarily cocommutative Hopf algebras over ground fields of arbitrary characteristic. Our proof uses the theory of support varieties for modules, one of the crucial ingredients being a tensor product property for some special modules. As an application, we prove a conjecture of Cibils stating that small quantum groups of rank at least two are wild.
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.
Uber Potenzsummenpolynome (On Polynomials Of Sums Of Power), Jorg Feldvoss
Uber Potenzsummenpolynome (On Polynomials Of Sums Of Power), Jorg Feldvoss
University Faculty and Staff Publications
No abstract provided.
Chief Factors And The Principal Block Of A Restricted Lie Algebra, Jorg Feldvoss
Chief Factors And The Principal Block Of A Restricted Lie Algebra, Jorg Feldvoss
University Faculty and Staff Publications
This paper is part of the conference proceedings from the conference titled The Monster and Lie Algebras that took place during a special research quarter at the Ohio State University in the spring of 1996. This conference was sponsored by the Ohio State University Mathematical Research Institute and the National Science Foundation. The focus of the conference was groups, Lie algebras, and the Monster, with emphasis on presenting the various aspects of group theory and Lie algebra theory from a modern perspective.
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.