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A triple construction for Lie bialgebras

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A triple construction for Lie bialgebras. / Grabowski, Jan.
In: Pacific Journal of Mathematics, Vol. 221, No. 2, 2005, p. 281-301.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Grabowski, J 2005, 'A triple construction for Lie bialgebras', Pacific Journal of Mathematics, vol. 221, no. 2, pp. 281-301. <http://msp.berkeley.edu/pjm/2005/221-2/p04.xhtml>

APA

Vancouver

Grabowski J. A triple construction for Lie bialgebras. Pacific Journal of Mathematics. 2005;221(2):281-301.

Author

Grabowski, Jan. / A triple construction for Lie bialgebras. In: Pacific Journal of Mathematics. 2005 ; Vol. 221, No. 2. pp. 281-301.

Bibtex

@article{0fc3a99e3ec54b03b41eb43e56c9aaf2,
title = "A triple construction for Lie bialgebras",
abstract = "We study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfel{\textquoteright}d double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the triple{\textquoteright}s algebraic structure, analogous to known results for the Drinfel{\textquoteright}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. ",
keywords = "Triple, Lie bialgebra, Drinfel'd double ",
author = "Jan Grabowski",
year = "2005",
language = "English",
volume = "221",
pages = "281--301",
journal = "Pacific Journal of Mathematics",
issn = "0030-8730",
publisher = "University of California, Berkeley",
number = "2",

}

RIS

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 -