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Examples of homotopy Lie algebras

Klaus Bering, Tom Lada (2009)

Archivum Mathematicum

We look at two examples of homotopy Lie algebras (also known as L algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators Δ to verify the homotopy Lie data is shown to produce the same results.

Exceptional collections on isotropic Grassmannians

Alexander Kuznetsov, Alexander Polishchuk (2016)

Journal of the European Mathematical Society

We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the Grothendieck group on homogeneous spaces of all classical groups.

Excision in entire cyclic cohomology

Ralf Meyer (2001)

Journal of the European Mathematical Society

We prove that entire and periodic cyclic cohomology satisfy excision for extensions of bornological algebras with a bounded linear section. That is, for such an extension we obtain a six term exact sequence in cohomology.

Existence of Gorenstein projective resolutions and Tate cohomology

Peter Jørgensen (2007)

Journal of the European Mathematical Society

Existence of proper Gorenstein projective resolutions and Tate cohomology is proved over rings with a dualizing complex. The proofs are based on Bousfield Localization which is originally a method from algebraic topology.

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