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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...

Twin trees I.

M.A. Ronan, J. Tits (1994)

Inventiones mathematicae

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 $f_{λ} : ℕ \to ℕ$ such that $f_{λ} (n) \geq n$ and $I n d_{f_{λ} (n)} (S^{λ} G)$ is an infinite set for every natural n > 1. In special cases $f_{λ} (ℕ)$ contains every natural number m >...