Corpus ID: 237592817

Separable equivalences, finitely generated cohomology and finite tensor categories

  title={Separable equivalences, finitely generated cohomology and finite tensor categories},
  author={Petter Andreas Bergh},
We show that finitely generated cohomology is invariant under separable equivalences for all algebras. As a result, we obtain a proof of the finite generation of cohomology for finite symmetric tensor categories in characteristic zero, as conjectured by Etingof and Ostrik. Moreover, for such categories we also determine the representation dimension and the Rouquier dimension of the stable category. Finally, we recover a number of results on the cohomology of stably equivalent and singularly… Expand


Radical cube zero weakly symmetric algebras and support varieties
Abstract One of our main results is a classification of all the weakly symmetric radical cube zero finite dimensional algebras over an algebraically closed field having a theory of support via theExpand
Cohomology of finite tensor categories: duality and Drinfeld centers
This work concerns the finite generation conjecture for finite tensor categories (Etingof and Ostrik '04), which proposes that for such a category C, the self-extension algebra of the unitExpand
Cohomology of twisted tensor products
Abstract It is well known that the cohomology of a tensor product is essentially the tensor product of the cohomologies. We look at twisted tensor products, and investigate to which extent this isExpand
Finite generation of Hochschild cohomology of Hecke algebras of finite classical type in characteristic zero
We show that the Hochschild cohomology HH*(ℋ) of a Hecke algebra ℋ of finite classical type over a field k of characteristic zero and a non-zero parameter q in k is finitely generated, unlessExpand
On the structure and cohomology ring of connected Hopf algebras
Abstract Let p be a prime, and k be a field of characteristic p. We investigate the algebra structure and the structure of the cohomology ring for the connected Hopf algebras of dimension p 3 , whichExpand
The representation dimension of Hecke algebras and symmetric groups
Abstract We establish a lower bound for the representation dimension of all the classical Hecke algebras of types A , B and D . For all the type A algebras, and “most” of the algebras of types B andExpand
Representation dimension of exterior algebras
We determine the representation dimension of exterior algebras. This provides the first known examples of representation dimension > 3. We deduce that the Loewy length of the group algebra over F2 ofExpand
Support varieties for any finite dimensional algebra over a field were introduced in (20) using graded subalgebras of the Hochschild cohomol- ogy. We mainly study these varieties for selfinjectiveExpand
Finite tensor categories
We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in ourExpand
Finiteness of representation dimension
We will show that any module over an artin algebra is a direct summand of some module whose endomorphism ring is quasi-hereditary. As a conclusion, any artin algebra has a finite representationExpand