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The Representation Theory of the Increasing Monoid

by Snowden, Andrew , Güntürkün, Sema

in 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

2023

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The Representation Theory of the Increasing Monoid

by Snowden, Andrew , Güntürkün, Sema

2023

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The Representation Theory of the Increasing Monoid

by Snowden, Andrew , Güntürkün, Sema

2023

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The Representation Theory of the Increasing Monoid

Snowden, Andrew,

Güntürkün, Sema

2023

Overview

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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Publisher

American Mathematical Society

Subject

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