scholarly journals On the Koszul property of toric face rings

2014 ◽  
Vol 6 (2) ◽  
pp. 233-259
Author(s):  
Dang Hop Nguyen
Keyword(s):  
Koszul Property

Standard Koszul self-injective special biserial algebras

2016 ◽  
Vol 15 (03) ◽  
pp. 1650044
Author(s):  
András Magyar
Keyword(s):  
Special Biserial Algebras ◽  
Koszul Property

The aim of this paper is to establish a connection between the standard Koszul and the quasi-Koszul property in the class of self-injective special biserial algebras. Furthermore, we give a characterization of standard Koszul symmetric special biserial algebras in terms of quivers and relations.

scholarly journals Symbolic powers of cover ideals of graphs and Koszul property

2021 ◽  
pp. 1-17
Author(s):  
Yan Gu ◽  
Huy Tài Hà ◽  
Joseph W. Skelton
Keyword(s):  
Vertex Cover ◽  
Cycle Cover ◽  
Symbolic Powers ◽  
Koszul Property

We show that attaching a whisker (or a pendant) at the vertices of a cycle cover of a graph results in a new graph with the following property: all symbolic powers of its cover ideal are Koszul or, equivalently, componentwise linear. This extends previous work where the whiskers were added to all vertices or to the vertices of a vertex cover of the graph.

scholarly journals A GENERALIZED KOSZUL PROPERTY FOR SKEW PBW EXTENSIONS

2017 ◽  
Vol 101 (2) ◽  
pp. 301-320 ◽  
Author(s):  
Héctor Suárez ◽  
Armando Reyes
Keyword(s):  
Koszul Property ◽  
Skew Pbw Extensions

scholarly journals The Koszul property for graded twisted tensor products

2018 ◽  
Vol 513 ◽  
pp. 50-90 ◽  
Author(s):  
Andrew Conner ◽  
Peter Goetz
Keyword(s):  
Tensor Products ◽  
Koszul Property

scholarly journals A new approach to the Koszul property in representation theory using graded subalgebras

2012 ◽  
Vol 12 (1) ◽  
pp. 153-197 ◽  
Author(s):  
Brian J. Parshall ◽  
Leonard L. Scott
Keyword(s):  
Positive Characteristic ◽  
Hereditary Algebra ◽  
New Approach ◽  
Schur Algebras ◽  
Graded Modules ◽  
Finite Dimensional ◽  
New Information ◽  
Koszul Property ◽  
Semisimple Algebraic Groups ◽  
Finite Dimensional Algebras

AbstractGiven a quasi-hereditary algebra $B$, we present conditions which guarantee that the algebra $\mathrm{gr} \hspace{0.167em} B$ obtained by grading $B$ by its radical filtration is Koszul and at the same time inherits the quasi-hereditary property and other good Lie-theoretic properties that $B$ might possess. The method involves working with a pair $(A, \mathfrak{a})$ consisting of a quasi-hereditary algebra $A$ and a (positively) graded subalgebra $\mathfrak{a}$. The algebra $B$ arises as a quotient $B= A/ J$ of $A$ by a defining ideal $J$ of $A$. Along the way, we also show that the standard (Weyl) modules for $B$ have a structure as graded modules for $\mathfrak{a}$. These results are applied to obtain new information about the finite dimensional algebras (e.g., the $q$-Schur algebras) which arise as quotients of quantum enveloping algebras. Further applications, perhaps the most penetrating, yield results for the finite dimensional algebras associated with semisimple algebraic groups in positive characteristic $p$. These results require, at least at present, considerable restrictions on the size of $p$.

scholarly journals Koszul property of diagonal subalgebras

2014 ◽  
Vol 6 (3) ◽  
pp. 385-406 ◽  
Author(s):  
Neeraj Kumar
Keyword(s):  
Koszul Property

scholarly journals Multigraded regularity and the Koszul property

2010 ◽  
Vol 323 (4) ◽  
pp. 1012-1017 ◽  
Author(s):  
Milena Hering
Keyword(s):  
Koszul Property

scholarly journals Quadratic Gorenstein rings and the Koszul property I

2020 ◽  
Vol 374 (2) ◽  
pp. 1077-1093 ◽  
Author(s):  
Matthew Mastroeni ◽  
Hal Schenck ◽  
Mike Stillman
Keyword(s):  
Gorenstein Rings ◽  
Koszul Property
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