scholarly journals The relative Hochschild-Serre spectral sequence and the Belkale-Kumar product

2013 ◽  
Vol 365 (11) ◽  
pp. 5833-5857 ◽  
Author(s):  
Sam Evens ◽  
William Graham
Keyword(s):  
Spectral Sequence ◽  
Serre Spectral Sequence

EXT ALGEBRA OF NICHOLS ALGEBRAS OF CARTAN TYPE A2

2013 ◽  
Vol 12 (04) ◽  
pp. 1250191
Author(s):  
XIAOLAN YU ◽  
YINHUO ZHANG
Keyword(s):  
Spectral Sequence ◽  
Hopf Algebras ◽  
Type A ◽  
Serre Spectral Sequence ◽  
Nichols Algebra ◽  
Cartan Type ◽  
Dynkin Diagrams ◽  
Full Structure ◽  
Pointed Hopf Algebras ◽  
Nichols Algebras

We give the full structure of the Ext algebra of any Nichols algebra of Cartan type A2 by using the Hochschild–Serre spectral sequence. As an application, we show that the pointed Hopf algebras [Formula: see text] with Dynkin diagrams of type A, D, or E, except for A1 and A1 × A1 with the order NJ > 2 for at least one component J, are wild.

scholarly journals A LERAY SPECTRAL SEQUENCE FOR NONCOMMUTATIVE DIFFERENTIAL FIBRATIONS

2013 ◽  
Vol 10 (05) ◽  
pp. 1350015 ◽  
Author(s):  
EDWIN BEGGS ◽  
IBTISAM MASMALI
Keyword(s):  
Spectral Sequence ◽  
Sheaf Cohomology ◽  
Left Module ◽  
Graded Algebras ◽  
Serre Spectral Sequence ◽  
Differential Graded Algebras ◽  
Zero Curvature ◽  
Total Differential ◽  
Leray Spectral Sequence ◽  
Special Case

This paper describes the Leray spectral sequence associated to a differential fibration. The differential fibration is described by base and total differential graded algebras. The cohomology used is noncommutative differential sheaf cohomology. For this purpose, a sheaf over an algebra is a left module with zero curvature covariant derivative. As a special case, we can recover the Serre spectral sequence for a noncommutative fibration.

scholarly journals The Serre spectral sequence of a multiplicative fibration

2001 ◽  
Vol 353 (9) ◽  
pp. 3803-3831 ◽  
Author(s):  
Yves Félix ◽  
Stephen Halperin ◽  
Jean-Claude Thomas
Keyword(s):  
Spectral Sequence ◽  
Serre Spectral Sequence

scholarly journals Nonabelian holomorphic Lie algebroid extensions

2015 ◽  
Vol 26 (05) ◽  
pp. 1550040 ◽  
Author(s):  
Ugo Bruzzo ◽  
Igor Mencattini ◽  
Vladimir N. Rubtsov ◽  
Pietro Tortella
Keyword(s):  
Line Bundle ◽  
Spectral Sequence ◽  
Lie Algebras ◽  
Hodge Structure ◽  
Lie Algebroids ◽  
Lie Algebroid ◽  
Serre Spectral Sequence ◽  
Atiyah Algebroid

We classify nonabelian extensions of Lie algebroids in the holomorphic category. Moreover we study a spectral sequence associated to any such extension. This spectral sequence generalizes the Hochschild–Serre spectral sequence for Lie algebras to the holomorphic Lie algebroid setting. As an application, we show that the hypercohomology of the Atiyah algebroid of a line bundle has a natural Hodge structure.

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