The Representation Theory of the Increasing Monoid

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...

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Bibliographic Details
Main Authors: Güntürkün, Sema, Snowden, Andrew
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2023
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Associative rings and algebras > Rings and algebras arising under various constructions > Quadratic and Koszul algebras msc
Commutative algebra
Commutative algebra > Computational aspects and applications > Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) msc
Commutative algebra > General commutative ring theory > None of the above, but in this section msc
Group theory and generalizations > Representation theory of groups > Representations of infinite symmetric groups msc
Monoids
Representations of categories
Symmetry groups
ISBN:9781470465469, 1470465469
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Summary: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.
Bibliography:June 2023, volume 286, number 1420 (fourth of 6 numbers)
Includes bibliographical references (p. 133-134)
ISBN:9781470465469
1470465469
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1420