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Super solutions of the dynamical Yang-Baxter equation

Author(s): Gizem Karaali
Journal: Proc. Amer. Math. Soc. 134 (2006), 2521-2531.
MSC (2000): Primary 17B37
Posted: March 22, 2006
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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

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

In this paper we classify super dynamical $ r-$matrices with zero weight.

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Additional Information:

Gizem Karaali
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: gizem@math.ucsb.edu

DOI: 10.1090/S0002-9939-06-08495-4
PII: S 0002-9939(06)08495-4
Keywords: Dynamical $r-$matrices, the dynamical Yang-Baxter equation, Lie superalgebras
Received by editor(s): March 31, 2005
Posted: March 22, 2006
Communicated by: Dan M. Barbasch
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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