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Ringel–Hall algebras and Lusztig's symmetries

✍ Scribed by Bangming Deng; Jie Xiao

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
151 KB
Volume
255
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let D(Λ) be the double Ringel-Hall algebra of a finite dimensional hereditary algebra Λ. The present paper shows that the BGP-reflection operators of D(Λ) coincide with Lusztig's symmetries (up to canonical isomorphisms) and satisfy the braid group relations on the whole double Ringel-Hall algebra D(Λ). This answers a question of

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