## 2-CATEGORICAL EXTENSION OF COHEN-MONTGOMERY DUALITY AND DERIVED EQUIVALENCES (Cohomology Theory of Finite Groups and Rel...

Published in Advances in Mathematics

Let G be a finite abelian group and A a G-graded algebra over a field of characteristic zero. This paper is devoted to a quantitative study of the graded polynomial identities satisfied by A. We study the asymptotic behavior of c n G ( A ) , n = 1 , 2 , … , the sequence of graded codimensions of A and we prove that if A satisfies an ordinary polyno...

Published in Advances in Mathematics

We describe some interesting graded rings which are generated by degree-3 elements inside the Sklyanin algebra S, and prove that they have many good properties. Geometrically, these rings R correspond to blowups of the Sklyanin P 2 at 7 or fewer points. We show that the rings R are exactly those degree-3-generated subrings of S which are maximal or...

Published in Advances in Mathematics

In this paper, we define a notion of AS-Gorenstein algebra for N -graded algebras, and show that symmetric AS-regular algebras of Gorenstein parameter 1 are exactly preprojective algebras of quasi-Fano algebras. This result can be compared with the fact that symmetric graded Frobenius algebras of Gorenstein parameter −1 are exactly trivial extensio...

Published in Advances in Mathematics

It is proved that over every countable field K there is a nil algebra R such that the algebra obtained from R by extending the field K contains noncommutative free subalgebras of arbitrarily high rank. It is also shown that over every countable field K there is an algebra R without noncommutative free subalgebras of rank two such that the algebra o...

Published in Advances in Mathematics

Let V be a finite set of divisorial valuations centered at a 2-dimensional regular local ring R. In this paper we study its structure by means of the semigroup of values, S V , and the multi-index graded algebra defined by V, gr V R . We prove that S V is finitely generated and we compute its minimal set of generators following the study of reduced...

Published in Open Mathematics

Let F be a field, and let R be a finitely-generated F-algebra, which is a domain with quadratic growth. It is shown that either the center of R is a finitely-generated F-algebra or R satisfies a polynomial identity (is PI) or else R is algebraic over F. Let r ∈ R be not algebraic over F and let C be the centralizer of r. It is shown that either the...

We study the topology of the boundary manifold of a regular neighborhood of a complex projective hypersurface. We show that, under certain Hodge theoretic conditions, the cohomology ring of the complement of the hypersurface functorially determines that of the boundary. When the hypersurface defines a hyperplane arrangement, the cohomology of the b...

Published in Advances in Mathematics

An infinite-dimensional N -graded k-algebra A is called projectively simple if dim k A / I

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