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- Title
Weak Quantum Enveloping Algebras of Borcherds Superalgebras.
- Authors
Zhixiang Wu
- Abstract
In present paper we define a new kind of weak quantized enveloping algebra $wU_{q}^{\tau}({\mathcal{G}})$ of Borcherds superalgebras ${\mathcal{G}}$ . It is a noncommutative and noncocommutative weak graded Hopf algebra. Using localizing with some Ore set, we obtain a different kind of quantized enveloping algebras of Borcherds superalgebras ${\mathcal{U}}_{q}({\mathcal{G}})$ . It has a homomorphic image which is isomorphic to the usual quantum enveloping algebra $U_{q}({\mathcal{G}})$ of ${\mathcal{G}}$ . Moreover, ${\mathcal{U}}_{q}({\mathcal{G}})$ is isomorphic to a direct sum of $U_{q}({\mathcal{G}})$ and an other algebra as algebras.
- Subjects
SUPERALGEBRAS; NONASSOCIATIVE algebras; QUANTUM theory; QUANTUM scattering; MATHEMATICAL analysis; ALGEBRAIC topology
- Publication
Acta Applicandae Mathematicae, 2009, Vol 106, Issue 2, p185
- ISSN
0167-8019
- Publication type
Article
- DOI
10.1007/s10440-008-9289-0