Yang-Baxter equation, Lie superalgebra, super dynamical r-matrices, zero weight condition, Hecke condition
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
[h ⊗ 1 + 1 ⊗ h, r(λ)] = 0 for all h ∈ ɧ, λ ∈ ɧ ∗ .
In this paper we explicitly quantize zero-weight super dynamical r-matrices with zero coupling constant for the Lie superalgebra 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.
© 2011 American Mathematical Society
Karaali, G., On the quantization of zero-weight super dynamical r-matrices, Proceedings of the American Mathematical Society, Volume 140 Issue 1 (January 2012), pages 7–20. MR2833513. doi: 10.1090/S0002-9939-2011-10873-6