On h-regular graded algebras
An elementary proof of the Weitzenböck Theorem
A decomposition theorem for complete comodule algebras over complete Hopf algebras
On h-regular grades algebras of characteristic p > 0
Basic properties of h-regular local Noetherian rings
Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants
Let H be a Hopf algebra over a field k such that every finite-dimensional (left) H-module is semisimple. We give a counterpart of the first fundamental theorem of the classical invariant theory for locally finite, finitely generated (commutative) H-module algebras, and for local, complete H-module algebras. Also, we prove that if H acts on the k-algebra A = k[[X₁,...,Xₙ]] in such a way that the unique maximal ideal in A is invariant, then the algebra of invariants is a noetherian Cohen-Macaulay...
A note on semisimple derivations of commutative algebras
A concept of a slice of a semisimple derivation is introduced. Moreover, it is shown that a semisimple derivation d of a finitely generated commutative algebra A over an algebraically closed field of characteristic 0 is nothing other than an algebraic action of a torus on Max(A), and, using this, that in some cases the derivation d is linearizable or admits a maximal invariant ideal.
Connected sequences of stable derived functors and their applications
CONTENTS1. Introduction........................................................................................................................................................................................................ 52. Category of complexes.................................................................................................................................................................................... 73. Left stable derived functors of covariant functors..........................................................................................................................................
The geometric reductivity of the quantum group
We introduce the concept of geometrically reductive quantum group which is a generalization of the Mumford definition of geometrically reductive algebraic group. We prove that if G is a geometrically reductive quantum group and acts rationally on a commutative and finitely generated algebra A, then the algebra of invariants is finitely generated. We also prove that in characteristic 0 a quantum group G is geometrically reductive if and only if every rational G-module is semisimple, and that in...
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