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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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
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Table of Contents:
  • 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