Finitely generated cohomology Hopf algebras
نویسندگان
چکیده
منابع مشابه
Finitely Generated Invariants of Hopf Algebras on Free Associative Algebras
We show that the invariants of a free associative algebra of finite rank under a linear action of a finite-dimensional Hopf algebra generated by group-like and skew-primitive elements form a finitely generated algebra exactly when the action is scalar. This generalizes an analogous result for group actions by automorphisms obtained by Dicks and Formanek, and Kharchenko.
متن کاملA reductive group with finitely generated cohomology algebras
Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H∗(G, A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductiv...
متن کامل4 A reductive group with finitely generated cohomology algebras .
Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H(G,A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductive ...
متن کاملCohomology of Hopf Algebras
Group algebras are Hopf algebras, and their Hopf structure plays crucial roles in representation theory and cohomology of groups. A Hopf algebra is an algebra A (say over a field k) that has a comultiplication (∆ : A → A ⊗k A) generalizing the diagonal map on group elements, an augmentation (ε : A → k) generalizing the augmentation on a group algebra, and an antipode (S : A → A) generalizing th...
متن کاملCohomology of Hopf C-algebras and Hopf von Neumann algebras
We will define two canonical cohomology theories for Hopf C∗-algebras and for Hopf von Neumann algebras (with coefficients in their comodules). We will then study the situations when these cohomologies vanish. The cases of locally compact groups and compact quantum groups will be considered in more details. 1991 AMS Mathematics Classification number: Primary: 46L55, 46L05; Secondary: 43A07, 22D25
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ژورنال
عنوان ژورنال: Topology
سال: 1970
ISSN: 0040-9383
DOI: 10.1016/0040-9383(70)90009-1