We will prove a Riemann–Roch like theorem for triangulated categories satisfying Serre
duality. As an application, we will prove Riemann–Roch Theorem and Adjunction Formula …

We construct algebras from rhombohedral tilings of Euclidean space obtained as projections
of certain cubical complexes. We show that these 'Cubist algebras' satisfy strong …

A Frobenius algebra over a field k is called symmetric if the Nakayama automorphism is an
inner automorphism. A stably symmetric algebra is defined to be a generalization of a …

Let A be a Frobenius Koszul algebra such that its Koszul dual A! is a quantum polynomial
algebra. Co-point modules over A were defined as dual notion of point modules over A! with …

A contravariant functor is constructed from the stable projective homotopy theory of finitely
generated graded modules over a finite-dimensional algebra to the derived category of its …

In this paper, we will use techniques of noncommutative projective geometry to construct
examples of algebras R over a field k not satisfying the following two types of symmetric …

This is the first of a pair of papers on homogeneous G-algebras. G-algebras, or Groebner
basis algebras, were studied by Levandosky, generalizing results by Apel and Berger. We …

As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet
relationship is also a guiding principle of non-commutative geometry known as Serre …

One of the major projects in noncommutative algebraic geometry is to classify
noncommutative curves and noncommutative surfaces [17]. The first half of this article will …

The main result of this announcement shows that, under Koszul duality between quiver
algebras, cohomology of tails is naturally isomorphic to stable cohomology. As an …