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Record Nr. |
UNINA9910960757703321 |
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Autore |
Margolis Stuart |
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Titolo |
Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry |
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Pubbl/distr/stampa |
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Providence : , : American Mathematical Society, , 2022 |
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©2021 |
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ISBN |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (154 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; v.274 |
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Classificazione |
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20M3016G1005E1052C3552C4016S3720M2552B0516E10 |
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Altri autori (Persone) |
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SaliolaFranco |
SteinbergBenjamin |
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Disciplina |
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Soggetti |
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CW complexes |
Semigroups |
Partially ordered sets |
Representations of algebras |
Combinatorial analysis |
Combinatorial geometry |
Group theory and generalizations -- Semigroups -- Representation of semigroups; actions of semigroups on sets |
Associative rings and algebras -- Representation theory of rings and algebras -- Representations of Artinian rings |
Combinatorics -- Algebraic combinatorics -- Combinatorial aspects of representation theory |
Convex and discrete geometry -- Discrete geometry -- Arrangements of points, flats, hyperplanes |
Convex and discrete geometry -- Discrete geometry -- Oriented matroids |
Associative rings and algebras -- Rings and algebras arising under various constructions -- Quadratic and Koszul algebras |
Group theory and generalizations -- Semigroups -- Semigroup rings, multiplicative semigroups of rings |
Convex and discrete geometry -- Polytopes and polyhedra -- Combinatorial properties (number of faces, shortest paths, etc.) |
Associative rings and algebras -- Homological methods -- Homological dimension |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"Volume 274, November 2021." |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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"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"-- |
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2. |
Record Nr. |
UNINA9910965757803321 |
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Autore |
Kechris A. S. <1946-> |
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Titolo |
Classical Descriptive Set Theory / / by Alexander Kechris |
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Pubbl/distr/stampa |
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New York, NY : , : Springer New York : , : Imprint : Springer, , 1995 |
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ISBN |
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Edizione |
[1st ed. 1995.] |
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Descrizione fisica |
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1 online resource (XVIII, 404 p.) |
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Collana |
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Graduate Texts in Mathematics, , 2197-5612 ; ; 156 |
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Disciplina |
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Soggetti |
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Logic, Symbolic and mathematical |
Topology |
Mathematical Logic and Foundations |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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I Polish Spaces -- 1. Topological and Metric Spaces -- 2. Trees -- 3. Polish Spaces -- 4. Compact Metrizable Spaces -- 5. Locally Compact Spaces -- 6. Perfect Polish Spaces -- 7.Zero-dimensional Spaces -- 8. Baire Category -- 9. Polish Groups -- II Borel Sets -- 10. Measurable Spaces and Functions -- 11. Borel Sets and Functions -- 12. Standard Borel Spaces -- 13. Borel Sets as Clopen Sets -- 14. Analytic Sets and the Separation Theorem -- 15. Borel Injections and Isomorphisms -- 16. Borel Sets and Baire Category -- 17. Borel Sets and Measures -- 18. Uniformization Theorems -- 19. Partition Theorems -- 20. Borel Determinacy -- 21. Games People Play -- 22. The Borel Hierarchy -- 23. Some Examples -- 24. The Baire Hierarchy -- III Analytic Sets -- 25. Representations of Analytic Sets -- 26. Universal and Complete Sets -- 27. Examples -- 28. Separation Theorems -- 29. Regularity Properties -- 30. Capacities -- 31. Analytic Well-founded Relations -- IV Co-Analytic Sets -- 32. Review -- 33. Examples -- 34. Co-Analytic Ranks -- 35. Rank Theory -- 36. Scales and Uniformiiatiou -- V Projective Sets -- 37. The Projective Hierarchy -- 38. Projective Determinacy -- 39. The Periodicity Theorems -- 40. Epilogue -- Appendix A. Ordinals and Cardinals -- Appendix B. Well-founded Relations -- Appendix C. On Logical Notation -- Notes and Hints -- References -- Symbols and Abbreviations. |
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Sommario/riassunto |
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Descriptive set theory has been one of the main areas of research in set |
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theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation. |
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