Document Type



Mathematics (Pomona)

Publication Date



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.

Rights Information

© 2011 American Mathematical Society

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Included in

Algebra Commons