Zhang, Pu
Published in
Advances in Mathematics

By introducing a twisted Hopf algebra we unify several important objects of study. Skew derivations of such an algebra are defined and the corresponding skew differential operator algebras are studied. This generalizes results in the Weyl algebra. Applying this investigation to the twisted Ringel–Hall algebra we get, in particular, a natural realiz...

Cohen, Daniel C. Suciu, Alexander I.

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...

Reichstein, Z. Rogalski, D. Zhang, J.J.
Published in
Advances in Mathematics

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

Smoktunowicz, Agata
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...

Delgado, F. Galindo, C. Núñez, A.
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...

Smoktunowicz, Agata
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...

Giambruno, A. La Mattina, D.
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...

Rogalski, D.
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...

Minamoto, Hiroyuki Mori, Izuru
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...

浅芝, 秀人