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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A triple construction for Lie bialgebras
AU - Grabowski, Jan
PY - 2005
Y1 - 2005
N2 - We study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfel’d double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the triple’s algebraic structure, analogous to known results for the Drinfel’d double: among them, that in the factorisable case the triple is isomorphic to a twisting of g ⊕ g ⊕ g by a certain cocycle. We also consider real forms of the triple and the triangular case.
AB - We study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfel’d double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the triple’s algebraic structure, analogous to known results for the Drinfel’d double: among them, that in the factorisable case the triple is isomorphic to a twisting of g ⊕ g ⊕ g by a certain cocycle. We also consider real forms of the triple and the triangular case.
KW - Triple
KW - Lie bialgebra
KW - Drinfel'd double
M3 - Journal article
VL - 221
SP - 281
EP - 301
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
SN - 0030-8730
IS - 2
ER -