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Displaying 821 – 840 of 859

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Troesch complexes and extensions of strict polynomial functors

Antoine Touzé (2012)

Annales scientifiques de l'École Normale Supérieure

We develop a new approach of extension calculus in the category of strict polynomial functors, based on Troesch complexes. We obtain new short elementary proofs of numerous classical Ext -computations as well as new results. In particular, we get a cohomological version of the “fundamental theorems” from classical invariant theory for  G L n for  n big enough (and we give a conjecture for smaller values of  n ). We also study the “twisting spectral sequence” E s , t ( F , G , r ) converging to the extension groups Ext 𝒫 𝕜 * ( F ( r ) , G ( r ) ) between the...

Twisted gamma filtration and algebras with orthogonal involution

Caroline Junkins (2014)

Open Mathematics

For the Grothendieck group of a split simple linear algebraic group, the twisted γ-filtration provides a useful tool for constructing torsion elements in -rings of twisted flag varieties. In this paper, we construct a non-trivial torsion element in the γ-ring of a complete flag variety twisted by means of a PGO-torsor. This generalizes the construction in the HSpin case previously obtained by Zainoulline.

Twisted group rings of strongly unbounded representation type

Leonid F. Barannyk, Dariusz Klein (2004)

Colloquium Mathematicae

Let S be a commutative local ring of characteristic p, which is not a field, S* the multiplicative group of S, W a subgroup of S*, G a finite p-group, and S λ G a twisted group ring of the group G and of the ring S with a 2-cocycle λ ∈ Z²(G,S*). Denote by I n d m ( S λ G ) the set of isomorphism classes of indecomposable S λ G -modules of S-rank m. We exhibit rings S λ G for which there exists a function f λ : such that f λ ( n ) n and I n d f λ ( n ) ( S λ G ) is an infinite set for every natural n > 1. In special cases f λ ( ) contains every natural number m >...

Currently displaying 821 – 840 of 859