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Diagrammatic algebra

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Diagrammatic algebra/ by Chris Bowman.
作者:	Bowman, Chris.
出版者:	Cham :Springer Nature Switzerland : : 2025.,
面頁冊數:	xxiv, 376 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Category Theory, Homological Algebra. -
電子資源:	https://doi.org/10.1007/978-3-031-88801-4
ISBN:	9783031888014

Diagrammatic algebra
Bowman, Chris.

Diagrammatic algebra[electronic resource] /by Chris Bowman. - Cham :Springer Nature Switzerland :2025. - xxiv, 376 p. :ill., digital ;24 cm. - Universitext,2191-6675. - Universitext..

Diagrammatic Algebra provides the intuition and tools necessary to address some of the key questions in modern representation theory, chief among them Lusztig's conjecture. This book offers a largely self-contained introduction to diagrammatic algebra, culminating in an explicit and entirely diagrammatic treatment of Geordie Williamson's explosive torsion counterexamples in full detail. The book begins with an overview of group theory and representation theory: first encountering Coxeter groups through their actions on puzzles, necklaces, and Platonic solids; then building up to non-semisimple representations of Temperley-Lieb and zig-zag algebras; and finally constructing simple representations of binary Schur algebras using the language of coloured Pascal triangles. Next, Kazhdan-Lusztig polynomials are introduced, with their study motivated by their combinatorial properties. The discussion then turns to diagrammatic Hecke categories and their associated p-Kazhdan-Lusztig polynomials, explored in a hands-on manner with numerous examples. The book concludes by showing that the problem of determining the prime divisors of Fibonacci numbers is a special case of the problem of calculating p-Kazhdan-Lusztig polynomials-using only elementary diagrammatic calculations and some manipulation of (5x5)-matrices. Richly illustrated and assuming only undergraduate-level linear algebra, this is a particularly accessible introduction to cutting-edge topics in representation theory. The elementary-yet-modern presentation will also be of interest to experts.

ISBN: 9783031888014

Standard No.: 10.1007/978-3-031-88801-4doiSubjects--Topical Terms:

678397
Category Theory, Homological Algebra.

LC Class. No.: QA155.5

Dewey Class. No.: 512.9

Diagrammatic algebra
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520 $a Diagrammatic Algebra provides the intuition and tools necessary to address some of the key questions in modern representation theory, chief among them Lusztig's conjecture. This book offers a largely self-contained introduction to diagrammatic algebra, culminating in an explicit and entirely diagrammatic treatment of Geordie Williamson's explosive torsion counterexamples in full detail. The book begins with an overview of group theory and representation theory: first encountering Coxeter groups through their actions on puzzles, necklaces, and Platonic solids; then building up to non-semisimple representations of Temperley-Lieb and zig-zag algebras; and finally constructing simple representations of binary Schur algebras using the language of coloured Pascal triangles. Next, Kazhdan-Lusztig polynomials are introduced, with their study motivated by their combinatorial properties. The discussion then turns to diagrammatic Hecke categories and their associated p-Kazhdan-Lusztig polynomials, explored in a hands-on manner with numerous examples. The book concludes by showing that the problem of determining the prime divisors of Fibonacci numbers is a special case of the problem of calculating p-Kazhdan-Lusztig polynomials-using only elementary diagrammatic calculations and some manipulation of (5x5)-matrices. Richly illustrated and assuming only undergraduate-level linear algebra, this is a particularly accessible introduction to cutting-edge topics in representation theory. The elementary-yet-modern presentation will also be of interest to experts.
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