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A Hopf Algebra from Preprojective Modules

Author
Li, Pak Hin
Abstract
Let Q be a finite type quiver i.e. ADE Dynkin quiver. Denote by \Lambda its preprojective algebra. It is known that there are finitely many indecomposable \Lambda-modules if and only if Q is of type A1, A2, A3, A4. Extending Lusztig’s construction of Un, we study an algebra generated by these indecomposable submodules. It turns out that it forms the universal enveloping algebra of some nilpotent Lie algebra inside the function algebra on Lusztig’s nilpotent scheme. The defining relations of the corresponding nilpotent Lie algebra for type A1, A2, A3, A4 are given here.
Description
45 pages
Date Issued
2020-05Subject
algebra; lie algebra; representation theory
Committee Chair
Knutson, Allen
Committee Member
Berest, Yuri; Stillman, Michael
Degree Discipline
Mathematics
Degree Name
Ph. D., Mathematics
Degree Level
Doctor of Philosophy
Type
dissertation or thesis