Journal of Nonlinear Mathematical Physics

Volume 6, Issue 4, November 1995, Pages 448 - 488

What a Classical r-Matrix Really Is

Authors
Boris A. KUPERSHMIDT
Corresponding Author
Boris A. KUPERSHMIDT
Available Online 1 November 1995.
DOI
https://doi.org/10.2991/jnmp.1999.6.4.5How to use a DOI?
Abstract
The notion of classical r-matrix is re-examined, and a definition suitable to differential (-difference) Lie algebras, ­ where the standard definitions are shown to be deficient, ­ is proposed, the notion of an O-operator. This notion has all the natural properties one would expect form it, but lacks those which are artifacts of finite-dimensional isomorpisms such as not true in differential generality relation End (V ) V V for a vector space V . Examples considered include a quadratic Poisson bracket on the dual space to a Lie algebra; generalized symplectic-quadratic models of such brackets (aka Clebsch representations); and Drinfel'd's 2-cocycle interpretation of nondegenate classical r-matrices.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
6 - 4
Pages
448 - 488
Publication Date
1995/11
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1999.6.4.5How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Boris A. KUPERSHMIDT
PY  - 1995
DA  - 1995/11
TI  - What a Classical r-Matrix Really Is
JO  - Journal of Nonlinear Mathematical Physics
SP  - 448
EP  - 488
VL  - 6
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1999.6.4.5
DO  - https://doi.org/10.2991/jnmp.1999.6.4.5
ID  - KUPERSHMIDT1995
ER  -