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010 a| 2022007678;

020 a| 9781470450427q| (paperback);

020 z| 9781470469146q| (epub);

035 a| (WaSeSS)ssj0002593203;

042 a| pcc;

049 a| EREEa| NEHH;

050 00 a| QA611.35b| .M37 2021;

082 00 a| 512/.272| 23/eng20220502;

084 a| 20M30a| 16G10a| 05E10a| 52C35a| 52C40a| 16S37a| 20M25a| 52B05a| 16E102| msc;

100 1 a| Margolis, Stuart,d| 1953-?| UNAUTHORIZED;

245 10 a| Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometryh| [electronic resource] /c| Stuart Margolis, Franco V. Saliola, Benjamin Steinberg.;

260 a| Providence, RI :b| American Mathematical Society,c| 2021.;

300 a| xi, 135 pages :b| illustrations ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| Number 1345;

500 a| "Volume 274, November 2021.";

504 a| Includes bibliographical references and index.;

505 0 a| Left regular bands, hyperplane arrangements, oriented matroids and generalizations -- Regular CW complexes and CW posets -- Algebras -- Projective resolutions and global dimension -- Quiver presentations -- Quadratic and Koszul duals -- Injective envelopes for hyperplane arrangements, oriented matroids, CAT(0) cube complexes and COMs -- Enumeration of cells for CW left regular bands -- Cohomological dimension.;

506 a| Available only to authorized users.;

520 a| "The purpose of the present monograph is to further develop and deepen the connection between left regular bands and poset topology. This allows us to compute finite projective resolutions of all simple modules of unital left regular band algebras over fields and much more. In the process, we are led to define the class of CW left regular bands as the class of left regular bands whose associated posets are the face posets of regular CW complexes. Most of the examples that have arisen in the literature belong to this class. A new and important class of examples is a left regular band structure on the face poset of a CAT(0) cube complex. Also, the recently introduced notion of a COM (complex of oriented matroids or conditional oriented matroid) fits nicely into our setting and includes CAT(0) cube complexes and certain more general CAT(0) zonotopal complexes. A fairly complete picture of the representation theory for CW left regular bands is obtained"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| CW complexes.=| ^A136128;

650 0 a| Semigroups.=| ^A52496;

650 0 a| Partially ordered sets.=| ^A163865;

650 0 a| Representations of algebras.=| ^A48799;

650 0 a| Combinatorial analysis.=| ^A31443;

650 0 a| Combinatorial geometry.=| ^A74137;

650 7 a| Group theory and generalizations -- Semigroups -- Representation of semigroups; actions of semigroups on sets.2| msc;

650 7 a| Associative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian rings.2| msc;

650 7 a| Combinatorics -- Algebraic combinatorics -- Combinatorial aspects of representation theory.2| msc;

650 7 a| Convex and discrete geometry -- Discrete geometry -- Arrangements of points, flats, hyperplanes.2| msc;

650 7 a| Convex and discrete geometry -- Discrete geometry -- Oriented matroids.2| msc;

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

650 7 a| Group theory and generalizations -- Semigroups -- Semigroup rings, multiplicative semigroups of rings.2| msc;

650 7 a| Convex and discrete geometry -- Polytopes and polyhedra -- Combinatorial properties (number of faces, shortest paths, etc.).2| msc;

650 7 a| Associative rings and algebras -- Homological methods -- Homological dimension.2| msc;

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

700 1 a| Saliola, Franco,d| 1977-?| UNAUTHORIZED;

700 1 a| Steinberg, Benjamin.=| ^A796435;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6852914;

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999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 6511983-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 1/14/2025x| EBOOKz| JERESOURCE;

Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry / Stuart Margolis, Franco V. Saliola, Benjamin Steinberg.

Author/creator	Margolis, Stuart, 1953-
Other author	Saliola, Franco, 1977-
Other author	Steinberg, Benjamin.
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, 2021.
Description	xi, 135 pages : illustrations ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	CW complexes. Semigroups. Partially ordered sets. Representations of algebras. Combinatorial analysis. Combinatorial geometry.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; Number 1345
Contents	Left regular bands, hyperplane arrangements, oriented matroids and generalizations -- Regular CW complexes and CW posets -- Algebras -- Projective resolutions and global dimension -- Quiver presentations -- Quadratic and Koszul duals -- Injective envelopes for hyperplane arrangements, oriented matroids, CAT(0) cube complexes and COMs -- Enumeration of cells for CW left regular bands -- Cohomological dimension.
Abstract	"The purpose of the present monograph is to further develop and deepen the connection between left regular bands and poset topology. This allows us to compute finite projective resolutions of all simple modules of unital left regular band algebras over fields and much more. In the process, we are led to define the class of CW left regular bands as the class of left regular bands whose associated posets are the face posets of regular CW complexes. Most of the examples that have arisen in the literature belong to this class. A new and important class of examples is a left regular band structure on the face poset of a CAT(0) cube complex. Also, the recently introduced notion of a COM (complex of oriented matroids or conditional oriented matroid) fits nicely into our setting and includes CAT(0) cube complexes and certain more general CAT(0) zonotopal complexes. A fairly complete picture of the representation theory for CW left regular bands is obtained"-- Provided by publisher.
General note	"Volume 274, November 2021."
Bibliography note	Includes bibliographical references and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022007678
ISBN	9781470450427 (paperback)
ISBN	(epub)

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Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry / Stuart Margolis, Franco V. Saliola, Benjamin Steinberg.

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