TL;DR: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints, which is shown to parallel the classical linear system theory in several ways.

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Abstract: This book proposes a unified mathematical treatment of a class of 'linear' discrete event systems, which contains important subclasses of Petri nets and queuing networks with synchronization constraints. The linearity has to be understood with respect to nonstandard algebraic structures, e.g. the 'max-plus algebra'. A calculus is developed based on such structures, which is followed by tools for computing the time behaviour to such systems. This algebraic vision lays the foundation of a bona fide 'discrete event system theory', which is shown to parallel the classical linear system theory in several ways.

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1,603 citations

Journal Article•10.1016/0040-9383(92)90015-A•

State sum invariants of 3 manifolds and quantum 6j symbols

[...]

Vladimir Turaev¹, Oleg Viro²•Institutions (2)

Centre national de la recherche scientifique¹, University of California, Riverside²

01 Oct 1992-Topology

TL;DR: In this article, a new approach to construct quantum invariants of 3-manifolds is presented, based on the so-called quantum 6j-symbols associated with the quantized universal enveloping algebra U,&(C) where CJ is a complex root of 1 of a certain degree z > 2.

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1,500 citations

Journal Article•10.1016/J.AIM.2005.06.003•

Tilting theory and cluster combinatorics

[...]

Aslak Bakke Buan¹, Robert J. Marsh², Markus Reineke³, Idun Reiten⁴, Gordana Todorov⁴ - Show less +1 more•Institutions (4)

Norwegian University of Science and Technology¹, University of Leicester², University of Münster³, Northeastern University⁴

20 Aug 2006-Advances in Mathematics

TL;DR: In this article, a new category C, called the cluster category, is introduced, which is obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field.

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1,163 citations

Book•

Topics in algebra

[...]

I. N. Herstein

1 Jan 1964

TL;DR: In this paper, the authors propose preliminary notions of group theory and group theory for group spaces and modules, including linear transformations and vector spaces. But they do not discuss group theory.

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Abstract: Preliminary Notions. Group Theory. Ring Theory. Vector Spaces and Modules. Fields. Linear Transformations. Selected Topics.

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1,047 citations

Journal Article•10.1007/BF01077848•