Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the quantization of zero-weight super dynamical $ r$-matrices


Author: Gizem Karaali
Journal: Proc. Amer. Math. Soc. 140 (2012), 7-20
MSC (2010): Primary 16T25; Secondary 17B37
Published electronically: May 5, 2011
MathSciNet review: 2833513
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical $ r$-matrices. A super dynamical $ r$-matrix $ r$ satisfies the zero weight condition if

$\displaystyle [h\otimes 1 + 1 \otimes h, r(\lambda)] = 0 \textmd{ for all } h \in \mathfrak{h}, \lambda \in \mathfrak{h}^*. $

In this paper we explicitly quantize zero-weight super dynamical $ r$-matrices with zero coupling constant for the Lie superalgebra $ \mathfrak{gl}(m,n)$. We also answer some questions about super dynamical $ R$-matrices. In particular, we prove a classification theorem and offer some support for one particular interpretation of the super Hecke condition.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 16T25, 17B37

Retrieve articles in all journals with MSC (2010): 16T25, 17B37


Additional Information

Gizem Karaali
Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711
Email: gizem.karaali@pomona.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10873-6
PII: S 0002-9939(2011)10873-6
Received by editor(s): February 11, 2010
Received by editor(s) in revised form: September 23, 2010, and October 31, 2010
Published electronically: May 5, 2011
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.