scholarly journals Artinian Level Algebras of Low Socle Degree

2013 ◽  
Vol 42 (2) ◽  
pp. 729-754 ◽  
Author(s):  
Alessandro De Stefani
Keyword(s):  
Level Algebras

scholarly journals Artinian level algebras of codimension 3

2012 ◽  
Vol 216 (1) ◽  
pp. 95-107 ◽  
Author(s):  
Jeaman Ahn ◽  
Yong Su Shin
Keyword(s):  
Level Algebras

scholarly journals Artinian level algebras of socle degree 4

2018 ◽  
Vol 507 ◽  
pp. 525-546 ◽  
Author(s):  
Shreedevi K. Masuti ◽  
M.E. Rossi
Keyword(s):  
Level Algebras

scholarly journals Minimal resolution of relatively compressed level algebras

2005 ◽  
Vol 284 (1) ◽  
pp. 333-370 ◽  
Author(s):  
Juan C. Migliore ◽  
Rosa M. Miró-Roig ◽  
Uwe Nagel
Keyword(s):  
Minimal Resolution ◽  
Level Algebras

scholarly journals Level Algebras and $\mathbf {s}$-Lecture Hall Polytopes

10.37236/8626 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Florian Kohl ◽  
McCabe Olsen
Keyword(s):  
Tangent Cones ◽  
Lecture Hall ◽  
Ehrhart Theory ◽  
Lattice Polytopes ◽  
The Family ◽  
Lecture Hall Partitions ◽  
Level Algebras

Given a family of lattice polytopes, a common endeavor in Ehrhart theory is the classification of those polytopes in the family that are Gorenstein, or more generally level. In this article, we consider these questions for ${\boldsymbol s}$-lecture hall polytopes, which are a family of simplices arising from $\mathbf {s}$-lecture hall partitions. In particular, we provide concrete classifications for both of these properties purely in terms of ${\boldsymbol s}$-inversion sequences. Moreover, for a large subfamily of ${\boldsymbol s}$-lecture hall polytopes, we provide a more geometric classification of the Gorenstein property in terms of  its tangent cones. We then show how one can use the classification of level ${\boldsymbol s}$-lecture hall polytopes to construct infinite families of level ${\boldsymbol s}$-lecture hall polytopes, and to describe level ${\boldsymbol s}$-lecture hall polytopes in small dimensions.

scholarly journals On parameter spaces for artin level algebras

2003 ◽  
Vol 51 (1) ◽  
pp. 187-208 ◽  
Author(s):  
Anthony Geramita ◽  
J. V. Chipalkatti
Keyword(s):  
Parameter Spaces ◽  
Level Algebras

On the Resolution of Certain Level Algebras

2004 ◽  
Vol 32 (11) ◽  
pp. 4221-4245 ◽  
Author(s):  
Massimo Brignone ◽  
Giuseppe Valla
Keyword(s):  
Level Algebras

scholarly journals DIVIDED POWER ALGEBRAS OVER AN OPERAD

2019 ◽  
Vol 62 (3) ◽  
pp. 477-517
Author(s):  
SACHA IKONICOFF
Keyword(s):  
Symmetric Group ◽  
The Other ◽  
Divided Power ◽  
Commutative Algebras ◽  
Level Algebras ◽  
Power Algebras

AbstractThe purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras. We describe these polynomial operations in two different ways: one way uses invariant elements under the action of the symmetric group and the other coinvariant elements. Our results are then applied to the case of level algebras, which are (non-associative) commutative algebras satisfying the exchange law.

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