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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Hlavní autori: Güntürkün, Sema, Snowden, Andrew
Médium: E-kniha Kniha
Jazyk:English
Vydavateľské údaje: Providence, Rhode Island American Mathematical Society 2023
Vydanie:1
Edícia:Memoirs of the American Mathematical Society
Predmet:
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
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Abstract 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.
AbstractList View the abstract.
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.
Author Snowden, Andrew
Güntürkün, Sema
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Notes June 2023, volume 286, number 1420 (fourth of 6 numbers)
Includes bibliographical references (p. 133-134)
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Snippet We study the representation theory of the increasing monoid. Our results provide a fairly comprehensive picture of the representation category: for example, we...
View the abstract.
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SubjectTerms 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
TableOfContents Introduction -- The increasing monoid -- Representation categories -- Monomial modules -- Gröbner theory -- Concatenation, shift, and transpose -- Finite length modules -- Multiplicities -- The smooth category as a Serre quotient of the graded category -- Completions -- The theorem on level -- Grothendieck groups, Hilbert series, and Krull dimension -- Induction and coinduction -- Injective modules -- Local cohomology and saturation -- Structure of level categories -- Koszul duality -- Grothendieck groups revisited -- Categorical background
Title The Representation Theory of the Increasing Monoid
URI https://www.ams.org/memo/1420/
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