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010 a| 2023031260;

020 a| 9781470465469q| (paperback);

020 z| 9781470475147q| (pdf);

035 a| (WaSeSS)ssj0002880767;

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084 a| 20C32a| 13A99a| 13P10a| 16S372| msc;

100 1 a| Gu¿˜ntu¿˜rku¿˜n, Sema.?| UNAUTHORIZED;

245 14 a| The representation theory of the increasing monoidh| [electronic resource] /c| Sema Gunturkun, Andrew Snowden.;

260 a| Providence, RI :b| American Mathematical Society,c| 2023.;

300 a| vii, 134 pages :b| illustrations ;c| 26 cm.;

504 a| Includes bibliographical references (pages 133-134).;

505 0 a| The increasing monoid -- Representation categories -- Monomial modules -- Gro¿˜bner 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.;

506 a| Available only to authorized users.;

520 a| "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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Monoids.=| ^A76789;

650 0 a| Symmetry groups.=| ^A49161;

650 0 a| Representations of categories.=| ^A349740;

650 0 a| Commutative algebra.=| ^A30350;

650 7 a| Group theory and generalizations -- Representation theory of groups -- Representations of infinite symmetric groups.2| msc;

650 7 a| Commutative algebra -- General commutative ring theory -- None of the above, but in this section.2| msc;

650 7 a| Commutative algebra -- Computational aspects and applications -- Gro¿˜bner bases; other bases for ideals and modules (e.g., Janet and border bases).2| msc;

650 7 a| Associative rings and algebras -- Rings and algebras arising under various constructions -- Quadratic and Koszul algebras.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Snowden, Andrew W.,d| 1982-?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30627636;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

949 a| CLICK ON WEB ADDRESSw| ASISh| HSL77;

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596 a| 1 3 4;

998 a| 6516069;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6516069-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 1/14/2025x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6516069-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

The representation theory of the increasing monoid / Sema Gunturkun, Andrew Snowden.

Author/creator	Gu¿˜ntu¿˜rku¿˜n, Sema
Other author	Snowden, Andrew W., 1982-
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2023.
Description	vii, 134 pages : illustrations ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Monoids. Symmetry groups. Representations of categories. Commutative algebra.

Contents	The increasing monoid -- Representation categories -- Monomial modules -- Gro¿˜bner 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.
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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 133-134).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2023031260
ISBN	9781470465469 (paperback)
ISBN	(pdf)

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