New York Journal of Mathematics
Volume 2 (1996) 35-58


Yorck Sommerhäuser

Deformed Enveloping Algebras

Published: April 8, 1996
Keywords: Deformed enveloping algebra, quantum group, smash product
Subject: 16W, 17B

We construct deformed enveloping algebras without using generators and relations via a generalized semidirect product construction. We give two Hopf algebraic constructions, the first one for general Hopf algebras with triangular decomposition and the second one for the special case that the outer tensorands are dual. The first construction generalizes Radford's biproduct and Majid's double crossproduct, the second one Drinfel'd's Double construction. The second construction is applied in the last section to construct deformed enveloping algebras in the setting created by G. Lusztig.

Author information

Universität München, Mathematisches Institut, Theresienstrasse 39, 80333 München, Germany