skip to main content

Attention:

The NSF Public Access Repository (NSF-PAR) system and access will be unavailable from 11:00 PM ET on Friday, November 15 until 2:00 AM ET on Saturday, November 16 due to maintenance. We apologize for the inconvenience.


Search for: All records

Award ID contains: 2001015

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. Zeev Rudnick (Ed.)
    Abstract

    We introduce the ozone group of a noncommutative algebra $A$, defined as the group of automorphisms of $A$, which fix every element of its center. In order to initiate the study of ozone groups, we study polynomial identity (PI) skew polynomial rings, which have long proved to be a fertile testing ground in noncommutative algebra. Using the ozone group and other invariants defined herein, we give explicit conditions for the center of a PI skew polynomial ring to be Gorenstein (resp. regular) in low dimension.

     
    more » « less
  2. Dan Abramovich (Ed.)

    LetAAbe a noetherian connected graded algebra. We introduce and study homological invariants that are weighted sums of the homological and internal degrees of cochain complexes of gradedAA-modules, providing weighted versions of Castelnuovo–Mumford regularity, Tor-regularity, Artin–Schelter regularity, and concavity. In some cases an invariant (such as Tor-regularity) that is infinite can be replaced with a weighted invariant that is finite, and several homological invariants of complexes can be expressed as weighted homological regularities. We prove a few weighted homological identities some of which unify different classical homological identities and produce interesting new ones.

     
    more » « less
  3. The Frobenius-Perron theory of an endofunctor of a k \Bbbk -linear category (recently introduced in Chen et al. [Algebra Number Theory 13 (2019), pp. 2005–2055]) provides new invariants for abelian and triangulated categories. Here we study Frobenius-Perron type invariants for derived categories of commutative and noncommutative projective schemes. In particular, we calculate the Frobenius-Perron dimension for domestic and tubular weighted projective lines, define Frobenius-Perron generalizations of Calabi-Yau and Kodaira dimensions, and provide examples. We apply this theory to the derived categories associated to certain Artin-Schelter regular and finite-dimensional algebras. 
    more » « less