The Representation Theory of the Increasing Monoid / Sema Güntürkün and Andrew Snowden.

Format:

Book

Author/Creator:

Güntürkün, Sema, author.

Snowden, Andrew W., 1982- author.

Series:

Memoirs of the American Mathematical Society ; Volume 286.

Memoirs of the American Mathematical Society Series ; Volume 286

Language:

English

Subjects (All):

Monoids.

Representations of categories.

Symmetry groups.

Commutative algebra.

Physical Description:

1 online resource (148 pages)

Edition:

First edition.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

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"-- Provided by publisher.

Contents:

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.

Notes:

Includes bibliographical references.

Description based on print version record.

Other Format:

Print version: Güntürkün, Sema The Representation Theory of the Increasing Monoid

ISBN:

9781470475147

1470475146