Characterizations of the quantum Witt algebra

✍ Scribed by Ke-Qin Liu

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 238 KB
• Volume: 24
• Category: Article
• ISSN: 0377-9017
• DOI: 10.1007/bf00420485

✦ Synopsis

The q-analogues of some concepts in the theory of nonassociative algebras are introduced and two characterizahons are gwen for the quantum Win algebra. (1991). 17A20, 17B65, 17B70.

Mathematics Subject Classifications

1. B a s i c D e f i n i t i o n s a n d M a i n T h e o r e m

In [1] and [3], two different characterizations of the Witt algebra were found by I. Kaplansky and M. L. Tomber, respectively. In this Letter, we prove that quantizations of these two characterizations hold for the quantum Witt algebra.

The following notations will be used throughout the Letter:

9 7/:= the set of all integers. 9 C : = the set of all complex numbers. 9 [ m ] . -q . . . . q '" 1 ' q -q where m 9 ~, q 9 C[0} and q is not a root of unity. 9

[1] for m 9 Z and m > 0 . q,,, + q m 9 ( m ) , = --2 where m 9 Z .