scholarly journals Spectral sequences for commutative Lie algebras

2020 ◽  
Vol 28 (2) ◽  
pp. 123-137
Author(s):  
Friedrich Wagemann
Keyword(s):  
Spectral Sequence ◽  
Lie Algebras ◽  
Spectral Sequences ◽  
Characteristic 2 ◽  
Leibniz Cohomology

AbstractWe construct some spectral sequences as tools for computing commutative cohomology of commutative Lie algebras in characteristic 2. In a first part, we focus on a Hochschild-Serre-type spectral sequence, while in a second part we obtain spectral sequences which compare Chevalley--Eilenberg-, commutative- and Leibniz cohomology. These methods are illustrated by a few computations.

scholarly journals Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Antieau ◽  
Bhargav Bhatt ◽  
Akhil Mathew
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Characteristic P ◽  
De Rham

Abstract We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

scholarly journals Bordered Floer homology and the spectral sequence of a branched double cover II: the spectral sequences agree

2016 ◽  
Vol 9 (2) ◽  
pp. 607-686
Author(s):  
Robert Lipshitz ◽  
Peter S. Ozsváth ◽  
Dylan P. Thurston
Keyword(s):  
Spectral Sequence ◽  
Floer Homology ◽  
Double Cover ◽  
Spectral Sequences

Motivic cohomology of quadrics and the coniveau spectral sequence

2010 ◽  
Vol 6 (3) ◽  
pp. 547-589 ◽  
Author(s):  
Nobuaki Yagita
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Motivic Cohomology

AbstractWe study the coniveau spectral sequence for quadrics defined by Pfister forms. In particular, we explicitly compute the motivic cohomology of anisotropic quadrics over ℝ, by showing that their coniveau spectral sequences collapse from the -term

Spectral Sequences

2020 ◽  
pp. 45-56
Author(s):  
Loring W. Tu
Keyword(s):  
Projective Plane ◽  
Spectral Sequence ◽  
Fiber Bundles ◽  
Spectral Sequences ◽  
Complex Projective Plane ◽  
Computational Tool ◽  
Short Introduction ◽  
Complex Projective

This chapter focuses on spectral sequences. The spectral sequence is a powerful computational tool in the theory of fiber bundles. First introduced by Jean Leray in the 1940s, it was further refined by Jean-Louis Koszul, Henri Cartan, Jean-Pierre Serre, and many others. The chapter provides a short introduction, without proofs, to spectral sequences. As an example, it computes the cohomology of the complex projective plane. The chapter then details Leray's theorem. A spectral sequence is like a book with many pages. Each time one turns a page, one obtains a new page that is the cohomology of the previous page.

New Simple Lie Algebras in Characteristic 2

2015 ◽  
Vol 2016 (18) ◽  
pp. 5695-5726 ◽  
Author(s):  
Sofiane Bouarroudj ◽  
Pavel Grozman ◽  
Alexei Lebedev ◽  
Dimitry Leites ◽  
Irina Shchepochkina
Keyword(s):  
Lie Algebras ◽  
Simple Lie Algebras ◽  
Characteristic 2

scholarly journals Centre-by-metabelian Lie algebras

1973 ◽  
Vol 15 (3) ◽  
pp. 259-264 ◽  
Author(s):  
M. R. Vaughan-Lee
Keyword(s):  
Recent Result ◽  
Lie Algebras ◽  
Basis Property ◽  
Finite Basis ◽  
Metabelian Groups ◽  
Finite Basis Property ◽  
Characteristic 2

If V is a variety of metabelian Lie algebras then V has a finite basis for its laws [3]. The proof of this result is similar to Cohen's proof that varieties of metabelian groups have the finite basis property [1]. However there are centre-by-metabelian Lie algebras of characteristic 2 which do not have a finite basis for their laws [4] this contrasts with McKay's recent result that varieties of centre-by-metabelian groups do have the finite basis property [2]. The rollowing theorem shows that once again “2” is the odd man out.

scholarly journals Deformations of current Lie algebras. I. Small algebras in characteristic 2

2017 ◽  
Vol 473 ◽  
pp. 513-544 ◽  
Author(s):  
Alexander Grishkov ◽  
Pasha Zusmanovich
Keyword(s):  
Lie Algebras ◽  
Characteristic 2
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