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This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many results and techniques not usually covered in introductory books, some of which appear here for the first time in book...
This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model...
This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the...
This monograph is devoted to a new class of non-commutative rings, skew Poincaré–Birkhoff–Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated projective modules over...
This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic. While strict...
This monograph presents combinatorial and numerical issues on integral quadratic forms as originally obtained in the context of representation theory of algebras and derived categories. Some of these beautiful results remain practically unknown to students and...
This monograph provides a comprehensive introduction to the Kazhdan-Lusztig theory of cells in the broader context of the unequal parameter case. Serving as a useful reference, the present volume offers a synthesis of significant advances made since Lusztig’s seminal...
This monograph is a comprehensive account of formal matrices, examining homological properties of modules over formal matrix rings and summarising the interplay between Morita contexts and K theory.While various special types of formal matrix rings have been studied for...
This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents...
In this monograph, the authors develop a new theory of p-adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology. Many major fundamental properties of these cohomology groups are proven,...
Translated from the popular French edition, this book offers a detailed introduction to various basic concepts, methods, principles, and results of commutative algebra. It takes a constructive viewpoint in commutative algebra and studies algorithmic approaches alongside...
Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further...
The most important invariant of a topological space is its fundamental group. When this is trivial, the resulting homotopy theory is well researched and familiar. In the general case, however, homotopy theory over nontrivial fundamental groups is much more problematic...
The theory of table algebras was introduced in 1991 by Z. Arad and H. Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups. Today, table algebra theory is a well-established branch of modern algebra with...
A Mathematician Said Who Can Quote Me a Theorem that’s True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick ?rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on ?eld invariants from the theory of quadratic...
The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical...
The ?rst aim of this work is to present the main results and methods of the theory of Noetherian semigroup algebras. These general results are then applied and illustrated in the context of certain interesting and important concrete classes of algebras that arise in a...
A principal ingredient in the proof of the Moonshine Theorem, connecting the Monster group to modular forms, is the infinite dimensional Lie algebra of physical states of a chiral string on an orbifold of a 26 dimensional torus, called the Monster Lie algebra. It is a...
The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information...
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