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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
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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.

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Additional Information

Gizem Karaali
Affiliation: Department of Mathematics, Pomona College, Claremont, California 91711

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.

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