The Representation Theory of the Increasing Monoid

被引：1
作者：
Gunturkun, Sema [1 ]
Snowden, Andrew [2 ]
机构：
[1] Univ Michigan, Ann Arbor, MI 48109 USA
[2] Univ Michigan, Dept Math, Ann Arbor, MI USA
来源：
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY | 2023年 / 286卷 / 1420期
关键词：
EQUIVARIANT HILBERT SERIES; HOMOLOGY; MODULES; STABILITY; IDEALS;
D O I：
10.1090/memo/1420
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we describe the Grothendieck group (including the effective cone), classify injective objects, establish properties of injective and projective resolutions, construct a derived auto-duality, and so on. Our work is motivated by numerous connections of this theory to other areas, such as representation stability, commutative algebra, simplicial theory, and shuffle algebras.
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页码：1 / 148
页数：148
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