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...

Full description

Saved in:
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
Tags: Add Tag
No Tags, Be the first to tag this record!
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
Author_xml – sequence: 1
  fullname: Güntürkün, Sema
– sequence: 2
  fullname: Snowden, Andrew
BackLink https://cir.nii.ac.jp/crid/1130860210910873873$$DView record in CiNii
BookMark eNo1kU1PGzEQht1CKhKaQ__BSuUAhy0zY-94faQRXxKoUkXPljexyyrJmq4XEP8eL0ml0Yw082i-3pk47GLnhfiG8APBwPnWb-M5KoJPYoZKg9IVKv4spmiULpkID8Tc6PqjxpVicyimAFyVhpgnYkZAEiQSw5fcQRqoDBojj8Q8pbaBimpWEvVU0MOjL377p94n3w1uaGNX5FTs34oYiiEXb7tl711qu7_Ffexiu_oqJsFtkp_v47H4c3X5sLgp735d3y4u7kpHUGlZLslpbYKqG2OwwkbRSjYrDK6Chr0J5FVokAJzU8uwUiSlG1fmOijUQR6Ls11fl9b-NT3GzZDsy8Y3Ma6T_X_9-Bmd2dMd-9THf88-DfYDW-aberexlz8XEpg0S87oyQ7t2tYu29EjSqgZKP8eodYyW8a-76dvk93PRLCjPHaUx47yyHfohXSn
CitedBy_id crossref_primary_10_1090_tran_9518
crossref_primary_10_1215_00127094_2024_0012
ContentType eBook
Book
Copyright Copyright 2023 American Mathematical Society
Copyright_xml – notice: Copyright 2023 American Mathematical Society
DBID RYH
DEWEY 512.2505
DOI 10.1090/memo/1420
DatabaseName CiNii Complete
DatabaseTitleList

DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISBN 1470475146
9781470475147
EISSN 1947-6221
Edition 1
ExternalDocumentID 9781470475147
EBC30627636
BD03492836
10_1090_memo_1420
GroupedDBID --Z
-~X
123
4.4
85S
ABPPZ
ACNCT
ACNUO
AEGFZ
AENEX
ALMA_UNASSIGNED_HOLDINGS
DU5
P2P
RMA
WH7
YNT
YQT
38.
AABBV
ABARN
ABQPQ
ADVEM
AERYV
AFOJC
AHWGJ
AJFER
BBABE
CZZ
GEOUK
RYH
ID FETCH-LOGICAL-a20573-c2a779f48b99151b42d3bd1fa50b6e9f2e4fb12f66b83fd4233a312668f417f3
ISBN 9781470465469
1470465469
ISICitedReferencesCount 2
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=0000061312&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0065-9266
IngestDate Fri Nov 08 02:35:23 EST 2024
Wed Dec 10 11:25:50 EST 2025
Thu Jun 26 22:38:27 EDT 2025
Thu Aug 14 15:25:31 EDT 2025
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
LCCN 2023031260
LCCallNum_Ident QA182 .G687 2023
Language English
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-a20573-c2a779f48b99151b42d3bd1fa50b6e9f2e4fb12f66b83fd4233a312668f417f3
Notes June 2023, volume 286, number 1420 (fourth of 6 numbers)
Includes bibliographical references (p. 133-134)
OCLC 1390591993
PQID EBC30627636
PageCount 148
ParticipantIDs askewsholts_vlebooks_9781470475147
proquest_ebookcentral_EBC30627636
nii_cinii_1130860210910873873
ams_ebooks_10_1090_memo_1420
PublicationCentury 2000
PublicationDate 2023.
PublicationDateYYYYMMDD 2023-01-01
PublicationDate_xml – year: 2023
  text: 2023.
PublicationDecade 2020
PublicationPlace Providence, Rhode Island
PublicationPlace_xml – name: Providence, Rhode Island
– name: Providence, RI
– name: Providence
PublicationSeriesTitle Memoirs of the American Mathematical Society
PublicationYear 2023
Publisher American Mathematical Society
Publisher_xml – name: American Mathematical Society
SSID ssib052864317
ssj0008047
ssj0002880767
ssib056432772
Score 2.6693246
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.
SourceID askewsholts
proquest
nii
ams
SourceType Aggregation Database
Publisher
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/
https://cir.nii.ac.jp/crid/1130860210910873873
https://ebookcentral.proquest.com/lib/[SITE_ID]/detail.action?docID=30627636
https://www.vlebooks.com/vleweb/product/openreader?id=none&isbn=9781470475147
Volume 286
WOSCitedRecordID wos0000061312&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELbYhQN74ikWWhQQ16h-xHFy4LLLUiRQQaKVeovixJaitg7abEv598w4cVLaA-KAtPLG1irOzhd5xuOZbwh5lyhNlapVbBS3sEFhaZzLRMQV6F7FpdBVT-L6RR0dZaen-behZlvnywko57Lr6_zHf4UaxgBsTJ39B7jHm8IAXAPo0ALs0N6yiMfuhLjnqAz5RK5PU_wV4gAahyaidw7A07Qhlv3y_SEel6_Wbtd_b8-GvneNmmnl_u7an8M6dSMQcvAZcHHLZzAdBo3UsEg90o7cI-MGkyWKIuNaX07lznJLc4xPvDAXrc_b53TSKmOs3-oDUuCAFZPOyEylsEG-f7j5evJ59IRxWEJg3GfdhdkCGVfoB06onB7gbAc4l-fG7RZkUXZnoBBAWeygN3NNc0evemPh-BGZYwLJY3LPuCdkMf357inhgFH0J0ZRj1HUWryKJoyiHqNn5OTj5nj9KR6qVsQlR3bJuOKlUrlNMg22t2Q64bXQNbOlpDo1ueUmsZpxm6Y6E7YGe1aUgoGhlNmEKSuek7lrnXlBolJgLWjNpJYGDGea1bYStSx1LjNumFySPZBA4Y_Vu6IPJ6AFCqhAAS3J2xuiKa7Ohx8GySowltWS7IPEiqrBloFFg0XJkC2WZkrAZ0neBFn2Ew1Bw8VmtRbIcZ2K9OVf7vGKPJzewj0y320vzT55UF3tmm77engffgM1JUCn
linkProvider ProQuest Ebooks
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.title=The+representation+theory+of+the+increasing+monoid&rft.au=G%C3%BCnt%C3%BCrk%C3%BCn%2C+Sema&rft.au=Snowden%2C+Andrew&rft.date=2023-01-01&rft.pub=American+Mathematical+Society&rft.isbn=9781470465469&rft_id=info:doi/10.1090%2Fmemo%2F1420&rft.externalDocID=BD03492836
thumbnail_m http://cvtisr.summon.serialssolutions.com/2.0.0/image/custom?url=https%3A%2F%2Fvle.dmmserver.com%2Fmedia%2F640%2F97814704%2F9781470475147.jpg