This article is available for purchase or by subscription. See below.
Abstract
|
For a finite-dimensional algebra
and a nonnegative integer
,
we characterize when the set
of additive equivalence classes of tilting modules with projective dimension at most
has a minimal
(or equivalently, minimum) element. This generalizes results of Happel and Unger. Moreover, for
an
-Gorenstein
algebra
with
, we construct a
minimal element in
.
As a result, we give equivalent conditions for a
-Gorenstein
algebra to be Iwanaga–Gorenstein. Moreover, for a
-Gorenstein algebra
and its factor algebra
, we show that there is
a bijection between
and the set
of additive equivalence classes of basic support
-tilting
-modules, where
is an idempotent
such that
is the additive generator of the category of projective-injective
-modules.
|
PDF Access Denied
We have not been able to recognize your IP address
3.133.123.99
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
$n$-Gorenstein algebra, tilting module, support
$\tau$-tilting module
|
Mathematical Subject Classification 2010
Primary: 16G10
Secondary: 16E10
|
Milestones
Received: 19 March 2018
Revised: 8 July 2018
Accepted: 14 July 2018
Published: 8 March 2019
|
|