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1 
Cohomology Operations and the Toral Rank Conjecture for Nilpotent Lie AlgebrasAmelotte, Steven 09 January 2013 (has links)
The action of various operations on the cohomology of nilpotent Lie algebras is studied. In the cohomology of any Lie algebra, we show that the existence of certain nontrivial compositions of higher cohomology operations implies the existence of hypercubelike structures in cohomology, which in turn establishes the Toral Rank Conjecture for that Lie algebra. We provide examples in low dimensions and exhibit an infinite family of nilpotent Lie algebras of arbitrary dimension for which such structures exist. A new proof of the Toral Rank Conjecture is also given for free twostep nilpotent Lie algebras.

2 
Cohomology Operations and the Toral Rank Conjecture for Nilpotent Lie AlgebrasAmelotte, Steven 09 January 2013 (has links)
The action of various operations on the cohomology of nilpotent Lie algebras is studied. In the cohomology of any Lie algebra, we show that the existence of certain nontrivial compositions of higher cohomology operations implies the existence of hypercubelike structures in cohomology, which in turn establishes the Toral Rank Conjecture for that Lie algebra. We provide examples in low dimensions and exhibit an infinite family of nilpotent Lie algebras of arbitrary dimension for which such structures exist. A new proof of the Toral Rank Conjecture is also given for free twostep nilpotent Lie algebras.

3 
Cohomology Operations and the Toral Rank Conjecture for Nilpotent Lie AlgebrasAmelotte, Steven January 2013 (has links)
The action of various operations on the cohomology of nilpotent Lie algebras is studied. In the cohomology of any Lie algebra, we show that the existence of certain nontrivial compositions of higher cohomology operations implies the existence of hypercubelike structures in cohomology, which in turn establishes the Toral Rank Conjecture for that Lie algebra. We provide examples in low dimensions and exhibit an infinite family of nilpotent Lie algebras of arbitrary dimension for which such structures exist. A new proof of the Toral Rank Conjecture is also given for free twostep nilpotent Lie algebras.

4 
Hopf algebras associated to transitive pseudogroups in codimension 2Cervantes, José Rodrigo 08 June 2016 (has links)
No description available.

5 
Invariantní differenciální operátory pro 1gradované geometrie / Invariant differential operators for 1graded geometriesTuček, Vít January 2017 (has links)
In this thesis we classify singular vectors in scalar parabolic Verma modules for those pairs (sl(n, C), p) of complex Lie algebras where the homogeneous space SL(n, C)/P is the Grassmannian of kplanes in Cn . We calculate cohomology of nilpotent radicals with values in certain unitarizable highest weight modules. According to [BH09] these modules have BGG resolutions with weights determined by this cohomology. Such resolutions induce complexes of invariant differential operators on sections of associated bundles over Hermitian symmetric spaces. We describe formal completions of unitarizable highest weight modules that one can use to modify method from [CD01] that constructs sequences of differential operators over any 1graded (aka almost Hermitian) geometry. We suggest uniform description of octonionic planes that could serve as a basis for better understanding of the exceptional Hermitian symmetric space for group E6.

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