Generic extensions and multiplicative bases of quantum groups at

Author:
Markus Reineke

Journal:
Represent. Theory **5** (2001), 147-163

MSC (2000):
Primary 17B37; Secondary 16G30

DOI:
https://doi.org/10.1090/S1088-4165-01-00111-X

Published electronically:
June 12, 2001

MathSciNet review:
1835003

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Abstract | References | Similar Articles | Additional Information

We show that the operation of taking generic extensions provides the set of isomorphism classes of representations of a quiver of Dynkin type with a monoid structure. Its monoid ring is isomorphic to the specialization at of Ringel's Hall algebra. This provides the latter algebra with a multiplicatively closed basis. Using a crystal-type basis for a two-parameter quantum group, this multiplicative basis is related to Lusztig's canonical basis.

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Additional Information

**Markus Reineke**

Affiliation:
BUGH Wuppertal, Gaußstr. 20, D-42097 Wuppertal, Germany

Email:
reineke@math.uni-wuppertal.de

DOI:
https://doi.org/10.1090/S1088-4165-01-00111-X

Received by editor(s):
August 14, 2000

Received by editor(s) in revised form:
April 10, 2001

Published electronically:
June 12, 2001

Article copyright:
© Copyright 2001
American Mathematical Society