Modules with 1-dimensional socle and components of Lusztig quiver varieties in type A
Joel Kamnitzer, Chandrika Sadanand
TL;DR
This paper classifies modules with 1-dimensional socle for type A preprojective algebras, analyzes their homomorphisms, and links them to the structure of Lusztig quiver varieties, advancing understanding of their geometric and algebraic properties.
Contribution
It provides a complete classification of modules with 1-dimensional socle and elucidates their role in describing Lusztig quiver variety components in type A.
Findings
Classified modules with 1-dimensional socle for type A preprojective algebras.
Determined all homomorphisms between these modules.
Connected these modules to the components of Lusztig quiver varieties.
Abstract
We study modules with 1-dimensional socle for preprojective algebras for type A quivers. In particular, we classify such modules, determine all homomorphisms between them, and then explain how they may be used to describe the components of Lusztig quiver varieties.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory