Finite-dimensional algebras and quivers
Alistair Savage
TL;DR
This paper provides an overview of finite-dimensional algebras and quivers, discussing key concepts like path algebras, Ringel-Hall algebras, and quiver varieties, aimed at readers interested in mathematical physics.
Contribution
It synthesizes fundamental topics on finite-dimensional algebras and quivers, highlighting their structures and applications in mathematical physics.
Findings
Summarizes the theory of path algebras and Ringel-Hall algebras.
Describes the construction and significance of quiver varieties by Lusztig and Nakajima.
Provides an integrated overview suitable for researchers in mathematical physics.
Abstract
This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of Lusztig and Nakajima.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons